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Math Problems
Grade 8
Write an equation word problem
1.5
a
−
4.5
b
=
3
(
a
+
b
)
5.5
b
=
5
(
b
−
a
)
+
2.5
a
\begin{aligned} 1.5 a-4.5 b & =3(a+b) \\ 5.5 b & =5(b-a)+2.5 a \end{aligned}
1.5
a
−
4.5
b
5.5
b
=
3
(
a
+
b
)
=
5
(
b
−
a
)
+
2.5
a
\newline
If
(
a
,
b
)
(a, b)
(
a
,
b
)
is the solution to the system of equations, then what is the value of
b
−
a
b-a
b
−
a
?
Get tutor help
Solve the system using inverse matrices.
\newline
{
9
x
+
6
y
=
0
x
+
y
=
−
1
\left\{\begin{array}{c} 9 x+6 y=0 \\ x+y=-1 \end{array}\right.
{
9
x
+
6
y
=
0
x
+
y
=
−
1
Get tutor help
Solve the following system of equations.
\newline
−
5
x
+
4
y
=
3
x
=
2
y
−
15
x
=
y
=
\begin{array}{l} -5 x+4 y=3 \\ \quad x=2 y-15 \\ x= \\ y= \end{array}
−
5
x
+
4
y
=
3
x
=
2
y
−
15
x
=
y
=
Get tutor help
Solve the system of equations.
\newline
3
x
+
4
y
=
−
23
x
=
3
y
+
1
x
=
y
=
\begin{array}{l} 3 x+4 y=-23 \\ x=3 y+1 \\ x= \\ y= \end{array}
3
x
+
4
y
=
−
23
x
=
3
y
+
1
x
=
y
=
Get tutor help
How many solutions does the system have?
\newline
{
20
x
−
5
y
=
5
4
x
−
y
=
1
\left\{\begin{array}{l} 20 x-5 y=5 \\ 4 x-y=1 \end{array}\right.
{
20
x
−
5
y
=
5
4
x
−
y
=
1
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
8
x
+
2
y
=
14
8
x
+
2
y
=
4
\begin{cases} 8x+2y=14 \ 8x+2y=4 \end{cases}
{
8
x
+
2
y
=
14
8
x
+
2
y
=
4
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
How many solutions does the system have?
\newline
{
y
=
4
x
−
8
4
y
=
4
x
−
8
\left\{\begin{array}{l} y=4 x-8 \\ 4 y=4 x-8 \end{array}\right.
{
y
=
4
x
−
8
4
y
=
4
x
−
8
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
4
x
+
5
y
=
12
5
x
+
7
y
=
14
\begin{array}{l} 4 x+5 y=12 \\ 5 x+7 y=14 \end{array}
4
x
+
5
y
=
12
5
x
+
7
y
=
14
\newline
solve for
y
y
y
Get tutor help
Solve for
m
m
m
.
\newline
3
−
2
(
9
+
2
m
)
=
m
m
=
\begin{array}{l} 3-2(9+2 m)=m \\ m= \end{array}
3
−
2
(
9
+
2
m
)
=
m
m
=
Get tutor help
Solve the following system of equations by elimination.
\newline
−
4
x
−
8
y
=
−
20
8
x
+
3
y
=
1
\begin{array}{c} -4 x-8 y=-20 \\ 8 x+3 y=1 \end{array}
−
4
x
−
8
y
=
−
20
8
x
+
3
y
=
1
Get tutor help
Solve the linear equation:
\newline
4
(
7
x
+
2
)
−
13
=
3
(
x
+
15
)
4(7x+2)-13=3(x+15)
4
(
7
x
+
2
)
−
13
=
3
(
x
+
15
)
,
\newline
x
=
x=
x
=
Get tutor help
How many solutions does the system have?
{
y
=
−
2
x
−
4
y
=
3
x
+
3
\begin{cases} y = -2x - 4 \newline\ y = 3x + 3 \end{cases}
{
y
=
−
2
x
−
4
y
=
3
x
+
3
Choose
1
1
1
answer:
\newline
(
A
)
(A)
(
A
)
Exactly one solution
\newline
(
B
)
(B)
(
B
)
No solutions
\newline
(
C
)
(C)
(
C
)
Infinitely many solutions
Get tutor help
`y=0.25x+12`
\newline
`y=K(x+3)`
\newline
In the system of equations,
\newline
K
K
K
is a constant. For which value of
\newline
K
K
K
does the system have no solution?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
0.25
0.25
0.25
\newline
(C)
0.75
0.75
0.75
\newline
(D)
12
12
12
Get tutor help
Find
x
x
x
and
y
y
y
.
\newline
2
x
+
8
y
=
6
2x+8y=6 \newline
2
x
+
8
y
=
6
5
x
+
20
y
=
15
5x+20y=15
5
x
+
20
y
=
15
Get tutor help
How many solutions does the system have?
\newline
{
y
=
−
2
x
−
4
y
=
3
x
+
3
\begin{cases} y=-2x-4\ \newline y=3x+3 \end{cases}
{
y
=
−
2
x
−
4
y
=
3
x
+
3
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
Get tutor help
6
x
+
2
y
=
3
6x+2y=3
6
x
+
2
y
=
3
\newline
6
x
+
y
=
3
6x+y=3
6
x
+
y
=
3
\newline
Consider the given system of equations. How many
(
x
,
y
)
(x,y)
(
x
,
y
)
solutions does this system have?
\newline
Choose
1
1
1
answer:
\newline
(A) No solutions
\newline
(B) Exactly one solution
\newline
(C) Infinitely many solutions
\newline
(D) None of the above
Get tutor help
Solve the system of equations by elimination method.
\newline
−
3
x
−
5
y
=
−
7
-3x-5y=-7
−
3
x
−
5
y
=
−
7
\newline
5
x
+
3
y
=
17
5x+3y=17
5
x
+
3
y
=
17
Get tutor help
Solve for
j
j
j
.
\newline
j
+
1
=
10
j+1= 10
j
+
1
=
10
\newline
j
=
j=
j
=
□
\square
□
Get tutor help
y
=
5
x
+
3
2
y
=
18
x
−
10
\begin{array}{c}y=5 x+3 \\ 2 y=18 x-10\end{array}
y
=
5
x
+
3
2
y
=
18
x
−
10
Get tutor help
Find the solution to the system of equations.
\newline
You can use the interactive graph below to find the solution.
\newline
{
y
=
−
4
x
−
3
y
=
−
2
x
+
1
x
=
y
=
\begin{array}{l} \left\{\begin{array}{l} y=-4 x-3 \\ y=-2 x+1 \end{array}\right. \\ x= \\ y= \end{array}
{
y
=
−
4
x
−
3
y
=
−
2
x
+
1
x
=
y
=
Get tutor help
Find the solution to the system of equations.
\newline
You can use the interactive graph below to find the solution.
\newline
{
y
=
−
2
x
+
7
y
=
5
x
−
7
x
=
□
y
=
□
\begin{array}{l} \left\{\begin{array}{l} y=-2 x+7 \\ y=5 x-7 \end{array}\right. \\ x=\square \\ y=\square \end{array}
{
y
=
−
2
x
+
7
y
=
5
x
−
7
x
=
□
y
=
□
Get tutor help
Find the solution to the system of equations.
\newline
You can use the interactive graph below to find the solution.
\newline
{
−
2
x
+
2
y
=
−
4
3
x
+
3
y
=
−
18
x
=
□
y
=
□
\begin{array}{l} \left\{\begin{array}{l} -2 x+2 y=-4 \\ 3 x+3 y=-18 \end{array}\right. \\ x=\square \\ y=\square \end{array}
{
−
2
x
+
2
y
=
−
4
3
x
+
3
y
=
−
18
x
=
□
y
=
□
Get tutor help
f
(
x
)
=
{
x
2
−
3
for
x
≠
0
−
5
for
x
=
0
f(x)=\left\{\begin{array}{lll} x^{2}-3 & \text { for } & x \neq 0 \\ -5 & \text { for } & x=0 \end{array}\right.
f
(
x
)
=
{
x
2
−
3
−
5
for
for
x
=
0
x
=
0
\newline
Find
f
(
0
)
f(0)
f
(
0
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
−
x
−
7
for
x
≠
−
3
4
for
x
=
−
3
f(x)=\left\{\begin{array}{lll} -x-7 & \text { for } & x \neq-3 \\ 4 & \text { for } & x=-3 \end{array}\right.
f
(
x
)
=
{
−
x
−
7
4
for
for
x
=
−
3
x
=
−
3
\newline
Find
f
(
0
)
f(0)
f
(
0
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
−
3
for
x
<
−
3
−
6
for
x
=
−
3
−
2
x
−
7
for
x
>
−
3
Find
f
(
−
8
)
\begin{array}{c} f(x)=\left\{\begin{array}{lll} -3 & \text { for } & x<-3 \\ -6 & \text { for } & x=-3 \\ -2 x-7 & \text { for } & x>-3 \end{array}\right. \\ \text { Find } f(-8) \end{array}
f
(
x
)
=
⎩
⎨
⎧
−
3
−
6
−
2
x
−
7
for
for
for
x
<
−
3
x
=
−
3
x
>
−
3
Find
f
(
−
8
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
−
6
for
x
≠
1
6
for
x
=
1
f(x)=\left\{\begin{array}{lll} -6 & \text { for } & x \neq 1 \\ 6 & \text { for } & x=1 \end{array}\right.
f
(
x
)
=
{
−
6
6
for
for
x
=
1
x
=
1
\newline
Find
f
(
−
6
)
f(-6)
f
(
−
6
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
x
−
1
for
−
2
≤
x
<
3
−
2
for
x
=
3
4
for
x
>
3
f(x)=\left\{\begin{array}{lll} x-1 & \text { for } & -2 \leq x<3 \\ -2 & \text { for } & x=3 \\ 4 & \text { for } & x>3 \end{array}\right.
f
(
x
)
=
⎩
⎨
⎧
x
−
1
−
2
4
for
for
for
−
2
≤
x
<
3
x
=
3
x
>
3
\newline
Find
f
(
4
)
f(4)
f
(
4
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
6
for
x
≠
5
1
for
x
=
5
f(x)=\left\{\begin{array}{lll} 6 & \text { for } & x \neq 5 \\ 1 & \text { for } & x=5 \end{array}\right.
f
(
x
)
=
{
6
1
for
for
x
=
5
x
=
5
\newline
Find
f
(
0
)
f(0)
f
(
0
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
2
x
−
1
for
x
≠
3
−
2
for
x
=
3
f(x)=\left\{\begin{array}{lll} 2 x-1 & \text { for } & x \neq 3 \\ -2 & \text { for } & x=3 \end{array}\right.
f
(
x
)
=
{
2
x
−
1
−
2
for
for
x
=
3
x
=
3
\newline
Find
f
(
3
)
f(3)
f
(
3
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
−
4
for
x
<
2
2
x
−
7
for
2
≤
x
<
7
2
x
−
7
for
x
≥
7
f(x)=\left\{\begin{array}{lll} -4 & \text { for } & x<2 \\ 2 x-7 & \text { for } & 2 \leq x<7 \\ 2 x-7 & \text { for } & x \geq 7 \end{array}\right.
f
(
x
)
=
⎩
⎨
⎧
−
4
2
x
−
7
2
x
−
7
for
for
for
x
<
2
2
≤
x
<
7
x
≥
7
\newline
Find
f
(
2
)
f(2)
f
(
2
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
−
x
−
7
for
x
≠
−
3
6
for
x
=
−
3
f(x)=\left\{\begin{array}{lll} -x-7 & \text { for } & x \neq-3 \\ 6 & \text { for } & x=-3 \end{array}\right.
f
(
x
)
=
{
−
x
−
7
6
for
for
x
=
−
3
x
=
−
3
\newline
Find
f
(
−
5
)
f(-5)
f
(
−
5
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
−
5
for
x
≠
4
−
6
for
x
=
4
f(x)=\left\{\begin{array}{lll} -5 & \text { for } & x \neq 4 \\ -6 & \text { for } & x=4 \end{array}\right.
f
(
x
)
=
{
−
5
−
6
for
for
x
=
4
x
=
4
\newline
Find
f
(
4
)
f(4)
f
(
4
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
−
x
+
3
for
x
≠
4
4
for
x
=
4
f(x)=\left\{\begin{array}{lll} -x+3 & \text { for } & x \neq 4 \\ 4 & \text { for } & x=4 \end{array}\right.
f
(
x
)
=
{
−
x
+
3
4
for
for
x
=
4
x
=
4
\newline
Find
f
(
4
)
f(4)
f
(
4
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
x
+
4
for
−
5
≤
x
<
1
−
2
for
x
=
1
−
(
x
−
1
)
2
+
6
for
1
<
x
≤
4
f(x)=\left\{\begin{array}{lll} x+4 & \text { for } & -5 \leq x<1 \\ -2 & \text { for } & x=1 \\ -(x-1)^{2}+6 & \text { for } & 1<x \leq 4 \end{array}\right.
f
(
x
)
=
⎩
⎨
⎧
x
+
4
−
2
−
(
x
−
1
)
2
+
6
for
for
for
−
5
≤
x
<
1
x
=
1
1
<
x
≤
4
\newline
Find
f
(
1
)
f(1)
f
(
1
)
\newline
Answer:
\newline
Get tutor help
f
(
x
)
=
{
(
x
+
5
)
2
−
8
for
x
≠
−
2
−
3
for
x
=
−
2
f(x)=\left\{\begin{array}{lll} (x+5)^{2}-8 & \text { for } & x \neq-2 \\ -3 & \text { for } & x=-2 \end{array}\right.
f
(
x
)
=
{
(
x
+
5
)
2
−
8
−
3
for
for
x
=
−
2
x
=
−
2
\newline
Find
f
(
−
2
)
f(-2)
f
(
−
2
)
\newline
Answer:
\newline
Get tutor help
x
=
2
y
+
5
y
=
(
2
x
−
3
)
(
x
+
9
)
\begin{array}{l} x=2 y+5 \\ y=(2 x-3)(x+9) \end{array}
x
=
2
y
+
5
y
=
(
2
x
−
3
)
(
x
+
9
)
\newline
How many ordered pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
satisfy the system of equations shown above?
\newline
A)
0
0
0
\newline
B)
1
1
1
\newline
C)
2
2
2
\newline
D) Infinitely many
Get tutor help
Solve the system of equations.
\newline
−
4
x
+
7
y
=
20
y
=
3
x
+
15
x
=
□
y
=
□
\begin{array}{l} -4 x+7 y=20 \\ y=3 x+15 \\ x=\square \\ y=\square \end{array}
−
4
x
+
7
y
=
20
y
=
3
x
+
15
x
=
□
y
=
□
Get tutor help
Solve the system of equations.
\newline
2
x
+
7
y
=
3
x
=
−
4
y
x
=
□
y
=
□
\begin{array}{l} 2 x+7 y=3 \\ x=-4 y \\ x=\square \\ y=\square \end{array}
2
x
+
7
y
=
3
x
=
−
4
y
x
=
□
y
=
□
Get tutor help
Solve the system of equations.
\newline
7
x
−
3
y
=
20
y
=
5
x
−
4
x
=
□
y
=
□
\begin{array}{l} 7 x-3 y=20 \\ y=5 x-4 \\ x=\square \\ y=\square \end{array}
7
x
−
3
y
=
20
y
=
5
x
−
4
x
=
□
y
=
□
Get tutor help
x
+
y
=
3
x
−
3
y
=
−
9
\begin{array}{c} x+y=3 \\ x-3 y=-9 \end{array}
x
+
y
=
3
x
−
3
y
=
−
9
\newline
What is the solution
(
x
,
y
)
(x, y)
(
x
,
y
)
to the given system of equations?
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Find the solution to the system of equations.
\newline
You can use the interactive graph below to find the solution.
\newline
{
y
=
−
7
x
+
3
y
=
−
x
−
3
x
=
y
=
\begin{array}{l} \left\{\begin{array}{l} y=-7 x+3 \\ y=-x-3 \end{array}\right. \\ x= \\ y= \end{array}
{
y
=
−
7
x
+
3
y
=
−
x
−
3
x
=
y
=
Get tutor help
Determine the intercepts of the line.
\newline
Do not round your answers.
\newline
−
7
x
−
6
y
=
−
15
y
-intercept:
(
□
,
□
)
x
-intercept:
(
□
,
□
)
\begin{array}{l} -7 x-6 y=-15 \\ y \text {-intercept: }(\square, \square) \\ x \text {-intercept: }(\square, \square) \end{array}
−
7
x
−
6
y
=
−
15
y
-intercept:
(
□
,
□
)
x
-intercept:
(
□
,
□
)
Get tutor help
{
g
(
1
)
=
4
g
(
n
)
=
g
(
n
−
1
)
+
3.2
g
(
3
)
=
□
\begin{array}{l}\left\{\begin{array}{l}g(1)=4 \\ g(n)=g(n-1)+3.2\end{array}\right. \\ g(3)=\square\end{array}
{
g
(
1
)
=
4
g
(
n
)
=
g
(
n
−
1
)
+
3.2
g
(
3
)
=
□
Get tutor help
Solve the system of linear equations and check any solutions algebraically. (If the the system is dependent, express
x
,
y
x, y
x
,
y
, and
z
z
z
in terms of the parameter a.)
\newline
{
x
−
3
y
+
2
z
=
18
5
x
−
13
y
+
12
z
=
100
\left\{\begin{array}{r} x-3 y+2 z=18 \\ 5 x-13 y+12 z=100 \end{array}\right.
{
x
−
3
y
+
2
z
=
18
5
x
−
13
y
+
12
z
=
100
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Solve the equation. Check your solution.
\newline
18
=
6
−
(
z
+
8
)
18=6-(z+8)
18
=
6
−
(
z
+
8
)
\newline
The solution set is
_
_
_
_
_
\_\_\_\_\_
_____
.
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Solve the system.
\newline
x
+
5
y
−
z
=
−
6
−
4
x
−
y
+
z
=
18
x
−
y
+
5
z
=
6
\begin{array}{rr} x+5 y-z= & -6 \\ -4 x-y+z= & 18 \\ x-y+5 z= & 6 \end{array}
x
+
5
y
−
z
=
−
4
x
−
y
+
z
=
x
−
y
+
5
z
=
−
6
18
6
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Solve the system by substitution.
\newline
9
x
−
y
=
−
30
y
=
−
x
\begin{aligned} 9 x-y & =-30 \\ y & =-x \end{aligned}
9
x
−
y
y
=
−
30
=
−
x
\newline
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
3
x
−
4
y
=
10
2
x
−
4
y
=
6
3x-4y=10 \\ 2x-4y=6
3
x
−
4
y
=
10
2
x
−
4
y
=
6
\newline
If
(
x
,
y
)
(x,y)
(
x
,
y
)
satisfies the given system of equations, what is the value of
y
y
y
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
10
\frac{1}{10}
10
1
\newline
(B)
1
2
\frac{1}{2}
2
1
\newline
(C)
16
5
\frac{16}{5}
5
16
\newline
(D)
4
4
4
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Find the solution of the system of equations.
\newline
4
x
−
8
y
=
16
8
x
−
9
y
=
39
\begin{array}{l} 4 x-8 y=16 \\ 8 x-9 y=39 \end{array}
4
x
−
8
y
=
16
8
x
−
9
y
=
39
\newline
Submit Answer
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Find the solution of the system of equations.
\newline
−
4
x
−
8
y
=
−
20
8
x
+
3
y
=
1
\begin{aligned} -4 x-8 y & =-20 \\ 8 x+3 y & =1 \end{aligned}
−
4
x
−
8
y
8
x
+
3
y
=
−
20
=
1
Get tutor help
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