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Math Problems
Grade 8
Solve a system of equations using any method
3
>
u
+
3
3
3>\frac{u+3}{3}
3
>
3
u
+
3
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Solve the system of equations.
\newline
3
x
−
2
y
=
6
x
+
y
=
−
8
\begin{array}{}3 x-2 y=6 \\ x+y=-8\end{array}
3
x
−
2
y
=
6
x
+
y
=
−
8
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
\newline
Two students in Mr. Terry's class, Britney and Francesca, have been assigned a workbook to complete at their own pace. They get together at Britney's house after school to complete as many pages as they can. Britney has already completed
13
13
13
pages and will continue working at a rate of
11
11
11
pages per hour. Francesca has completed
27
27
27
pages and can work at a rate of
9
9
9
pages per hour. Eventually, the two students will be working on the same page. How long will that take? How many pages will each of them have completed?
\newline
After
_
\_
_
hours, Britney and Francesca will have each completed
_
\_
_
pages in their workbooks.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
\newline
The members of a cooking club are making cakes, which they will sell at a street fair for
$
23
\$23
$23
apiece. It cost
$
20
\$20
$20
for a booth at the fair, and the ingredients for each cake cost
$
3
\$3
$3
. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How many cakes will they have sold? How much will the sales and expenditures be?
\newline
Once the members of the club have sold _____ cakes, they will break even, with sales and expenditures of
$
\$
$
_____.
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Which of the following is a rational number?
\newline
Choices:
\newline
(A)
π
\pi
π
\newline
(B)
1.27
1.27
1.27
\newline
(C)
7
\sqrt{7}
7
\newline
(D)
3
\sqrt{3}
3
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Which of the following is an irrational number?
\newline
Choices:
\newline
(A)
π
\pi
π
\newline
(B)
4
4
4
\newline
(C)
0
0
0
\newline
(D)
5
5
5
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Solve.
\newline
8
x
+
3
y
=
−
11
8x + 3y = -11
8
x
+
3
y
=
−
11
\newline
y
=
−
9
y = -9
y
=
−
9
\newline
(_____, _____)
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Solve.
\newline
7
x
−
10
y
=
20
7x - 10y = 20
7
x
−
10
y
=
20
\newline
y
=
−
9
y = -9
y
=
−
9
\newline
(_____, _____)
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Solve.
\newline
8
x
−
8
y
=
16
8x - 8y = 16
8
x
−
8
y
=
16
\newline
x
=
8
x = 8
x
=
8
\newline
(_____, _____)
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Solve.
\newline
5
x
+
6
y
=
20
5x + 6y = 20
5
x
+
6
y
=
20
\newline
x
=
−
8
x = -8
x
=
−
8
\newline
(_____, _____)
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Solve.
\newline
x
=
6
x = 6
x
=
6
\newline
6
x
+
9
y
=
18
6x + 9y = 18
6
x
+
9
y
=
18
\newline
(_____, _____)
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The principal's new car cost
$
35
,
000
\$ 35,000
$35
,
000
, but in three years it will only be worth
$
21
,
494
\$ 21,494
$21
,
494
. Write an equation for this situation and explain what each part of the equation represents in the context of the problem. What is the annual rate of depreciation?
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4
x
+
8
y
=
20
4x+8y=20
4
x
+
8
y
=
20
\newline
−
4
x
+
2
y
=
−
30
-4x+2y=-30
−
4
x
+
2
y
=
−
30
\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
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1
1
1
)
2
log
6
u
−
8
log
6
v
2 \log _{6} u-8 \log _{6} v
2
lo
g
6
u
−
8
lo
g
6
v
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3
x
+
y
=
13
2
x
+
2
y
=
18
\begin{array}{l}3 x+y=13 \\ 2 x+2 y=18\end{array}
3
x
+
y
=
13
2
x
+
2
y
=
18
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
\newline
Mr. Mitchell is contemplating which chauffeured car service to take to the airport. The first costs
$
29
\$29
$29
up front and
$
1
\$1
$1
per kilometer. The second costs
$
7
\$7
$7
plus
$
2
\$2
$2
per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? What is the total fare?
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
\newline
Mr. Mitchell is contemplating which chauffeured car service to take to the airport. The first costs
$
29
\$29
$29
up front and
$
1
\$1
$1
per kilometer. The second costs
$
7
\$7
$7
plus
$
2
\$2
$2
per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? What is the total fare?
\newline
For a driving distance of
km
\text{km}
km
, the total fare is
$
□
\$\square
$
□
.
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Which expressions are equivalent to
z
+
(
z
+
6
)
z+(z+6)
z
+
(
z
+
6
)
?
\newline
Choose all answers that apply:
\newline
A)
(
z
+
z
)
+
(
z
+
6
)
(z+z)+(z+6)
(
z
+
z
)
+
(
z
+
6
)
\newline
B)
(
z
+
6
)
+
6
(z+6)+6
(
z
+
6
)
+
6
\newline
C)
2
(
z
+
3
)
2(z+3)
2
(
z
+
3
)
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Which expressions are equivalent to
2
(
−
6
c
+
3
)
+
4
c
2(-6c+3)+4c
2
(
−
6
c
+
3
)
+
4
c
?
\newline
Choose all answers that apply:
\newline
A)
−
8
c
+
6
-8c+6
−
8
c
+
6
\newline
B)
3
(
−
4
c
+
2
)
+
4
c
3(-4c+2)+4c
3
(
−
4
c
+
2
)
+
4
c
\newline
C) None of the above
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