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Math Problems
Grade 8
Write an equation word problem
Find the solution of the system of equations.
\newline
3
x
−
6
y
=
−
45
x
−
6
y
=
−
47
\begin{array}{r} 3 x-6 y=-45 \\ x-6 y=-47 \end{array}
3
x
−
6
y
=
−
45
x
−
6
y
=
−
47
\newline
(_________,________)
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Find the solution of the system of equations.
\newline
9
x
+
y
=
−
12
7
x
+
y
=
−
10
\begin{array}{l} 9 x+y=-12 \\ 7 x+y=-10 \end{array}
9
x
+
y
=
−
12
7
x
+
y
=
−
10
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
−
3
x
+
4
y
=
−
7
3
x
+
6
y
=
27
\begin{aligned} -3 x+4 y & =-7 \\ 3 x+6 y & =27 \end{aligned}
−
3
x
+
4
y
3
x
+
6
y
=
−
7
=
27
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
−
3
x
−
8
y
=
−
25
6
x
+
8
y
=
10
\begin{aligned} -3 x-8 y & =-25 \\ 6 x+8 y & =10 \end{aligned}
−
3
x
−
8
y
6
x
+
8
y
=
−
25
=
10
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
−
4
x
+
3
y
=
−
19
−
4
x
+
6
y
=
−
10
\begin{array}{l} -4 x+3 y=-19 \\ -4 x+6 y=-10 \end{array}
−
4
x
+
3
y
=
−
19
−
4
x
+
6
y
=
−
10
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
8
x
−
5
y
=
−
14
−
8
x
+
y
=
22
\begin{array}{l} 8 x-5 y=-14 \\ -8 x+y=22 \end{array}
8
x
−
5
y
=
−
14
−
8
x
+
y
=
22
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
9
x
+
4
y
=
47
−
9
x
−
y
=
−
32
\begin{array}{l} 9 x+4 y=47 \\ -9 x-y=-32 \end{array}
9
x
+
4
y
=
47
−
9
x
−
y
=
−
32
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
−
8
x
+
9
y
=
39
8
x
−
10
y
=
−
46
\begin{aligned} -8 x+9 y & =39 \\ 8 x-10 y & =-46 \end{aligned}
−
8
x
+
9
y
8
x
−
10
y
=
39
=
−
46
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
3
x
+
9
y
=
27
−
3
x
−
5
y
=
−
23
\begin{aligned} 3 x+9 y & =27 \\ -3 x-5 y & =-23 \end{aligned}
3
x
+
9
y
−
3
x
−
5
y
=
27
=
−
23
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
3
x
+
7
y
=
−
2
4
x
−
7
y
=
−
19
\begin{array}{l} 3 x+7 y=-2 \\ 4 x-7 y=-19 \end{array}
3
x
+
7
y
=
−
2
4
x
−
7
y
=
−
19
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
−
8
x
−
3
y
=
−
24
−
8
x
−
6
y
=
0
\begin{array}{l} -8 x-3 y=-24 \\ -8 x-6 y=0 \end{array}
−
8
x
−
3
y
=
−
24
−
8
x
−
6
y
=
0
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
−
10
x
+
9
y
=
−
4
3
x
−
9
y
=
−
24
\begin{aligned} -10 x+9 y & =-4 \\ 3 x-9 y & =-24 \end{aligned}
−
10
x
+
9
y
3
x
−
9
y
=
−
4
=
−
24
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
−
5
x
+
5
y
=
−
35
−
5
x
+
8
y
=
−
50
\begin{array}{l} -5 x+5 y=-35 \\ -5 x+8 y=-50 \end{array}
−
5
x
+
5
y
=
−
35
−
5
x
+
8
y
=
−
50
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
7
x
+
2
y
=
27
9
x
+
2
y
=
37
\begin{array}{l} 7 x+2 y=27 \\ 9 x+2 y=37 \end{array}
7
x
+
2
y
=
27
9
x
+
2
y
=
37
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
6
x
+
4
y
=
−
46
6
x
+
6
y
=
−
42
\begin{array}{l} 6 x+4 y=-46 \\ 6 x+6 y=-42 \end{array}
6
x
+
4
y
=
−
46
6
x
+
6
y
=
−
42
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
2
x
−
3
y
=
−
1
2
x
+
y
=
19
\begin{array}{c} 2 x-3 y=-1 \\ 2 x+y=19 \end{array}
2
x
−
3
y
=
−
1
2
x
+
y
=
19
\newline
(_________,________)
Get tutor help
Find the solution of the system of equations.
\newline
x
−
4
y
=
6
x
−
6
y
=
12
\begin{array}{l} x-4 y=6 \\ x-6 y=12 \end{array}
x
−
4
y
=
6
x
−
6
y
=
12
\newline
\newline
(_________,________)
Get tutor help
Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
1
2
(
4
x
+
4
)
+
9
=
7
x
+
2
(
−
2
x
+
2
)
\frac{1}{2}(4 x+4)+9=7 x+2(-2 x+2)
2
1
(
4
x
+
4
)
+
9
=
7
x
+
2
(
−
2
x
+
2
)
\newline
Get tutor help
Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
−
2
(
10
x
−
7
)
−
7
=
−
3
(
7
x
−
1
)
−
8
-2(10 x-7)-7=-3(7 x-1)-8
−
2
(
10
x
−
7
)
−
7
=
−
3
(
7
x
−
1
)
−
8
\newline
Get tutor help
Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
9
x
−
4
−
3
=
3
(
3
x
−
3
)
+
2
9 x-4-3=3(3 x-3)+2
9
x
−
4
−
3
=
3
(
3
x
−
3
)
+
2
\newline
Get tutor help
Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
−
2
(
5
x
+
9
)
−
4
=
4
+
5
(
−
2
x
−
5
)
-2(5 x+9)-4=4+5(-2 x-5)
−
2
(
5
x
+
9
)
−
4
=
4
+
5
(
−
2
x
−
5
)
\newline
Get tutor help
Solve for
b
b
b
.
\newline
4
b
−
8
3
=
2
b
b
=
[
?
]
\begin{array}{c} \frac{4 b-8}{3}=2 b \\ b=[?] \end{array}
3
4
b
−
8
=
2
b
b
=
[
?]
Get tutor help
Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
3
(
−
2
x
−
5
)
=
−
6
x
−
15
3(-2 x-5)=-6 x-15
3
(
−
2
x
−
5
)
=
−
6
x
−
15
\newline
Get tutor help
Solve the system of equations.
\newline
{
4
x
−
y
=
11
6
x
−
2
y
=
13
\left\{\begin{array}{l}4 x-y=11 \\ 6 x-2 y=13\end{array}\right.
{
4
x
−
y
=
11
6
x
−
2
y
=
13
Get tutor help
Solve the equation. Check your solutions. Write your solutions from least to greatest, separated by a comma, if necessary.
\newline
−
x
2
−
12
=
−
8
x
-x^{2}-12=-8 x
−
x
2
−
12
=
−
8
x
\newline
x
=
□
,
□
x = \square , \square
x
=
□
,
□
Get tutor help
Solve the system of equations.
\newline
{
y
=
−
6
x
+
4
y
=
1
4
x
−
4
\left\{\begin{array}{l}y=-6 x+4 \\ y=\frac{1}{4} x-4\end{array}\right.
{
y
=
−
6
x
+
4
y
=
4
1
x
−
4
Get tutor help
Which best represents the solution set for the inequality
−
3
x
+
9
≥
−
21
-3 x+9 \geq-21
−
3
x
+
9
≥
−
21
?
\newline
(A)
x
≥
10
x \geq 10
x
≥
10
\newline
(B)
x
≤
10
x \leq 10
x
≤
10
\newline
(C)
x
≥
−
4
x \geq-4
x
≥
−
4
\newline
(D)
x
≤
−
4
x \leq-4
x
≤
−
4
Get tutor help
1
3
x
=
9
y
−
1
3
x
=
2
\begin{array}{c} \frac{1}{3} x=9 \\ y-\frac{1}{3} x=2 \end{array}
3
1
x
=
9
y
−
3
1
x
=
2
\newline
The system of equations above has solution
(
x
,
y
)
(x, y)
(
x
,
y
)
. What is the value of
y
y
y
?
\newline
(A)
9
2
\frac{9}{2}
2
9
\newline
(B)
11
2
\frac{11}{2}
2
11
\newline
(C)
7
7
7
\newline
(D)
11
11
11
Get tutor help
6
x
+
2
y
=
3
6
x
+
y
=
3
\begin{array}{l} 6 x+2 y=3 \\ 6 x+y=3 \end{array}
6
x
+
2
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
\newline
(D) None of the above
Get tutor help
12
t
=
4
v
−
3
−
6
t
=
4
v
+
6
\begin{array}{r} 12 t=4 v-3 \\ -6 t=4 v+6 \end{array}
12
t
=
4
v
−
3
−
6
t
=
4
v
+
6
\newline
If
(
t
,
v
)
(t, v)
(
t
,
v
)
is the solution to the system of equations, what is the value of
t
−
v
t-v
t
−
v
?
\newline
□
\square
□
Get tutor help
Find the sum. Give your answer as a simplified mixed number.
\newline
12
4
9
+
5
1
3
[
□
]
[
□
]
[
□
]
\begin{array}{c} 12 \frac{4}{9}+5 \frac{1}{3} \\ {[\square] \frac{[\square]}{[\square]}} \end{array}
12
9
4
+
5
3
1
[
□
]
[
□
]
[
□
]
Get tutor help
25
25
25
.
2
w
−
3
z
=
−
1
3
w
+
4
z
=
24
\begin{array}{l}2 w-3 z=-1 \\ 3 w+4 z=24\end{array}
2
w
−
3
z
=
−
1
3
w
+
4
z
=
24
Get tutor help
y
=
−
x
−
3
y
=
1
3
x
+
5
\begin{array}{l}y=-x-3 \\ y=\frac{1}{3} x+5\end{array}
y
=
−
x
−
3
y
=
3
1
x
+
5
Get tutor help
y
=
4
x
2
−
4
x
+
6
y=4 x^{2}-4 x+6
y
=
4
x
2
−
4
x
+
6
Get tutor help
5
N
=
0.01
(
N
−
76
)
5N =0.01(N-76)
5
N
=
0.01
(
N
−
76
)
Get tutor help
Solve the following equation and check your solution.
\newline
11
x
+
7
−
4
=
10
x
−
2
x
=
□
\begin{array}{l} 11 x+7-4=10 x-2 \\ x=\square \end{array}
11
x
+
7
−
4
=
10
x
−
2
x
=
□
Get tutor help
Solve using elimination.
\newline
−
7
x
−
6
y
=
16
−
8
x
−
9
y
=
−
1
\begin{array}{l} -7 x-6 y=16 \\ -8 x-9 y=-1 \end{array}
−
7
x
−
6
y
=
16
−
8
x
−
9
y
=
−
1
\newline
(
_
_
_
_
_
,
_
_
_
_
_
)
(\_\_\_\_\_, \_\_\_\_\_)
(
_____
,
_____
)
Get tutor help
Given the following system of equations, find the value of
y
y
y
:
\newline
4
y
+
14
x
=
10
−
2
y
−
4
x
=
4
\begin{array}{l} 4 y+14 x=10 \\ -2 y-4 x=4 \end{array}
4
y
+
14
x
=
10
−
2
y
−
4
x
=
4
Get tutor help
Solve by the elimination method.
\newline
9
x
−
6
y
=
19
−
6
x
+
4
y
=
11
\begin{array}{r} 9 x-6 y=19 \\ -6 x+4 y=11 \end{array}
9
x
−
6
y
=
19
−
6
x
+
4
y
=
11
Get tutor help
Solve the system algebraically:
\newline
y
=
2
x
−
3
y
=
6
x
+
1
\begin{array}{l} y=2 x-3 \\ y=6 x+1 \end{array}
y
=
2
x
−
3
y
=
6
x
+
1
Get tutor help
6
x
−
2
y
=
10
3
x
−
y
=
2
\begin{array}{l} 6 x-2 y=10 \\ 3 x-y=2 \\\end{array}
6
x
−
2
y
=
10
3
x
−
y
=
2
Get tutor help
−
x
−
5
y
+
z
=
17
−
5
x
−
5
y
+
5
z
=
5
2
x
+
5
y
−
3
z
=
−
10
\begin{array}{l} -x-5 y+z=17 \\ -5 x-5 y+5 z=5 \\ 2 x+5 y-3 z=-10 \end{array}
−
x
−
5
y
+
z
=
17
−
5
x
−
5
y
+
5
z
=
5
2
x
+
5
y
−
3
z
=
−
10
Get tutor help
y
=
−
4
x
−
10
−
5
x
−
2
y
=
11
\begin{array}{l}y=-4 x-10 \\ -5 x-2 y=11\end{array}
y
=
−
4
x
−
10
−
5
x
−
2
y
=
11
Get tutor help
−
2
x
−
9
y
=
−
25
−
4
x
−
9
y
=
−
23
\begin{aligned}-2 x-9 y & =-25 \\ -4 x-9 y & =-23\end{aligned}
−
2
x
−
9
y
−
4
x
−
9
y
=
−
25
=
−
23
Get tutor help
How many solutions does the system have?
\newline
{
3
x
+
y
=
8
2
x
+
2
y
=
8
\left\{\begin{array}{l} 3 x+y=8 \\ 2 x+2 y=8 \end{array}\right.
{
3
x
+
y
=
8
2
x
+
2
y
=
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
+
b
x
=
2
x
+
3
(
x
+
1
)
-4+bx=2x+3(x+1)
−
4
+
b
x
=
2
x
+
3
(
x
+
1
)
\newline
In the equation shown,
b
b
b
is a constant. For what value of
b
b
b
does the equation have no solutions?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
3
3
\newline
(B)
4
4
4
\newline
(C)
5
5
5
\newline
(D)
6
6
6
Get tutor help
What is the solution to this system of equations?
\newline
{
x
+
3
y
−
z
=
6
4
x
−
2
y
+
2
z
=
−
10
6
x
+
z
=
−
12
\left\{\begin{array}{c} x+3 y-z=6 \\ 4 x-2 y+2 z=-10 \\ 6 x+z=-12 \end{array}\right.
⎩
⎨
⎧
x
+
3
y
−
z
=
6
4
x
−
2
y
+
2
z
=
−
10
6
x
+
z
=
−
12
Get tutor help
{
y
=
x
−
4
y
=
4
x
+
2
\left\{\begin{array}{l}y=x-4 \\ y=4 x+2\end{array}\right.
{
y
=
x
−
4
y
=
4
x
+
2
\newline
x
=
y
=
\begin{array}{l}x= \\ y=\end{array}
x
=
y
=
Get tutor help
{
−
8
x
+
4
y
=
24
−
7
x
+
7
y
=
28
x
=
\begin{array}{l}\left\{\begin{array}{l}-8 x+4 y=24 \\ -7 x+7 y=28\end{array}\right. \\ x=\end{array}
{
−
8
x
+
4
y
=
24
−
7
x
+
7
y
=
28
x
=
Get tutor help
The given system of equations has solution
\newline
(
x
,
y
)
(x,y)
(
x
,
y
)
. What is the value of
\newline
x
x
x
?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
\text{(A)}\ 4
(A)
4
\newline
(B)
5
\text{(B)}\ 5
(B)
5
\newline
(C)
8
\text{(C)}\ 8
(C)
8
\newline
(D)
20
\text{(D)}\ 20
(D)
20
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