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Math Problems
Grade 8
Write an equation word problem
A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
\newline
10
x
−
8
y
=
−
12
4
x
+
8
y
=
96
\begin{array}{c} 10 x-8 y=-12 \\ 4 x+8 y=96 \end{array}
10
x
−
8
y
=
−
12
4
x
+
8
y
=
96
\newline
Add to eliminate
x
\mathbf{x}
x
.
\newline
Subtract to eliminate
y
\mathbf{y}
y
.
\newline
Add to eliminate
y
\mathbf{y}
y
.
\newline
Subtract to eliminate
x
\mathbf{x}
x
.
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A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
\newline
−
5
x
−
10
y
=
−
140
−
5
x
−
3
y
=
−
77
\begin{aligned} -5 x-10 y & =-140 \\ -5 x-3 y & =-77 \end{aligned}
−
5
x
−
10
y
−
5
x
−
3
y
=
−
140
=
−
77
\newline
Add to eliminate
y
\mathbf{y}
y
.
\newline
Subtract to eliminate
x
\mathbf{x}
x
.
\newline
Add to eliminate
x
\mathbf{x}
x
.
\newline
Subtract to eliminate
y
\mathbf{y}
y
.
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A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
\newline
5
x
−
7
y
=
−
58
−
9
x
+
7
y
=
54
\begin{aligned} 5 x-7 y & =-58 \\ -9 x+7 y & =54 \end{aligned}
5
x
−
7
y
−
9
x
+
7
y
=
−
58
=
54
\newline
Subtract to eliminate
y
\mathbf{y}
y
.
\newline
Add to eliminate
x
\mathbf{x}
x
.
\newline
Subtract to eliminate
x
\mathbf{x}
x
.
\newline
Add to eliminate
y
\mathbf{y}
y
.
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
x
+
6
y
=
−
6
2
x
+
13
y
=
−
10
\begin{aligned} x+6 y & =-6 \\ 2 x+13 y & =-10 \end{aligned}
x
+
6
y
2
x
+
13
y
=
−
6
=
−
10
\newline
No Solutions
\newline
Infinitely Many Solutions
\newline
One Solution
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
−
x
+
2
y
=
−
1
5
x
−
10
y
=
5
\begin{aligned} -x+2 y & =-1 \\ 5 x-10 y & =5 \end{aligned}
−
x
+
2
y
5
x
−
10
y
=
−
1
=
5
\newline
One Solution
\newline
Infinitely Many Solutions
\newline
No Solutions
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
−
x
+
y
=
3
−
2
x
+
2
y
=
3
\begin{array}{r} -x+y=3 \\ -2 x+2 y=3 \end{array}
−
x
+
y
=
3
−
2
x
+
2
y
=
3
\newline
No Solutions
\newline
Infinitely Many Solutions
\newline
One Solution
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
x
+
y
=
−
9
−
x
−
y
=
9
\begin{aligned} x+y & =-9 \\ -x-y & =9 \end{aligned}
x
+
y
−
x
−
y
=
−
9
=
9
\newline
No Solutions
\newline
Infinitely Many Solutions
\newline
One Solution
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
4
x
+
y
=
4
−
6
x
−
y
=
−
6
\begin{array}{c} 4 x+y=4 \\ -6 x-y=-6 \end{array}
4
x
+
y
=
4
−
6
x
−
y
=
−
6
\newline
One Solution
\newline
Infinitely Many Solutions
\newline
No Solutions
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
−
2
x
+
y
=
−
5
2
x
−
y
=
5
\begin{aligned} -2 x+y & =-5 \\ 2 x-y & =5 \end{aligned}
−
2
x
+
y
2
x
−
y
=
−
5
=
5
\newline
No Solutions
\newline
Infinitely Many Solutions
\newline
One Solution
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
x
+
3
y
=
7
x
−
3
y
=
−
10
\begin{array}{l} x+3 y=7 \\ x-3 y=-10 \end{array}
x
+
3
y
=
7
x
−
3
y
=
−
10
\newline
One Solution
\newline
Infinitely Many Solutions
\newline
No Solutions
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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
x
+
6
y
=
8
−
x
−
6
y
=
−
8
\begin{aligned} x+6 y & =8 \\ -x-6 y & =-8 \end{aligned}
x
+
6
y
−
x
−
6
y
=
8
=
−
8
\newline
No Solutions
\newline
One Solution
\newline
Infinitely Many Solutions
Get tutor help
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\newline
x
+
6
y
=
1
−
2
x
−
12
y
=
−
3
\begin{aligned} x+6 y & =1 \\ -2 x-12 y & =-3 \end{aligned}
x
+
6
y
−
2
x
−
12
y
=
1
=
−
3
\newline
One Solution
\newline
Infinitely Many Solutions
\newline
No Solutions
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The equations are graphed in the
x
y
xy
x
y
-plane. Which equation's graph will have a slope of
7
8
\frac{7}{8}
8
7
and a
y
y
y
intercept of
3
3
3
?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
x
+
8
y
=
24
7x+8y=24
7
x
+
8
y
=
24
\newline
(B)
7
x
−
8
y
=
−
24
7x-8y=-24
7
x
−
8
y
=
−
24
\newline
(C)
8
x
+
7
y
=
3
8x+7y=3
8
x
+
7
y
=
3
\newline
(D)
7
x
−
8
y
=
3
7x-8y=3
7
x
−
8
y
=
3
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Solve the equation.
\newline
27
=
15
+
n
n
=
□
\begin{array}{l} 27 = 15 + n \\ n = \square \end{array}
27
=
15
+
n
n
=
□
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Solve.
\newline
7
(
2
z
−
4
)
=
0
7(2 z-4)=0
7
(
2
z
−
4
)
=
0
\newline
Answer:
z
=
z=
z
=
\newline
Submit Answer
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Complete the recursive formula of the arithmetic sequence
\newline
4
,
22
,
40
,
58
,
…
4, 22, 40, 58, \dots
4
,
22
,
40
,
58
,
…
.
\newline
b
(
1
)
=
□
b(1)=\square
b
(
1
)
=
□
\newline
b
(
n
)
=
b
(
n
−
1
)
+
□
b(n) = b(n-1) +\square
b
(
n
)
=
b
(
n
−
1
)
+
□
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{
g
(
x
)
=
3
x
−
7
h
(
x
)
=
2
−
g
(
x
)
\begin{cases} g(x)=3x-7 \ h(x)=2-g(x) \end{cases}
{
g
(
x
)
=
3
x
−
7
h
(
x
)
=
2
−
g
(
x
)
\newline
The functions
g
g
g
and
h
h
h
are defined. What is the value of
h
(
1
)
h(1)
h
(
1
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\text{(A)}
(A)
6
6
6
\newline
(B)
\text{(B)}
(B)
1
1
1
\newline
(C)
\text{(C)}
(C)
−
2
-2
−
2
\newline
(D)
\text{(D)}
(D)
−
6
-6
−
6
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{
6
5
p
+
k
q
=
4
5
q
=
3
5
p
−
2
5
\begin{cases} \frac{6}{5}p + kq = \frac{4}{5} \ q = \frac{3}{5}p - \frac{2}{5} \end{cases}
{
5
6
p
+
k
q
=
5
4
q
=
5
3
p
−
5
2
Consider the system of equations, where
k
k
k
is a constant. For which value of
k
k
k
is there no
(
p
,
q
)
(p,q)
(
p
,
q
)
solutions?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2
-2
−
2
\newline
(B)
0
0
0
\newline
(C)
2
2
2
\newline
(D) None of the above
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Which value of
k
k
k
makes
5
−
k
+
12
=
16
5-k+12=16
5
−
k
+
12
=
16
a true statement?
\newline
Choose
1
1
1
answer:
\newline
(A)
k
=
1
k=1
k
=
1
\newline
(B)
k
=
2
k=2
k
=
2
\newline
(C)
k
=
3
k=3
k
=
3
\newline
(D)
k
=
4
k=4
k
=
4
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Solve for
k
k
k
.
k
4
=
3
8
\frac{k}{4}=\frac{3}{8}
4
k
=
8
3
\newline
k
=
□
k=\square
k
=
□
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How many solutions does the system have?
\newline
{
y
=
−
7
x
+
8
y
=
−
7
x
−
8
\begin{cases} y = -7x + 8 \\ y = -7x - 8 \end{cases}
{
y
=
−
7
x
+
8
y
=
−
7
x
−
8
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
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How many solutions does the system have?
\newline
{
y
=
−
5
x
+
1
y
=
1
−
5
x
\begin{cases} y=-5x+1 \ y=1-5x \end{cases}
{
y
=
−
5
x
+
1
y
=
1
−
5
x
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly one solution
\newline
(B) No solutions
\newline
(C) Infinitely many solutions
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Solve for
p
p
p
.
\newline
\begin{align*} 9(p-4)&=-18,\ p&=\Box \end{align*}
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Solve the equation.
\newline
11
=
7
v
v
=
□
\begin{array}{l} 11=7v \ v=\square \end{array}
11
=
7
v
v
=
□
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Solve the equation.
\newline
\begin{align*} \frac{w}{5} &= 3,\ w &= \Box \end{align*}
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Solve the equation. \begin{align*} 2 &= \frac{n}{3}, \ n &= \square \end{align*}
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Solve for
k
k
k
.
k
6
=
4
3
k
=
□
\begin{array}{l}\frac{k}{6}=\frac{4}{3} \\k=\square\end{array}
6
k
=
3
4
k
=
□
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Solve for
k
k
k
.
(
3
k
)
=
(
4
5
)
k
=
□
\begin{align*} \left(\frac{3}{k}\right)&=\left(\frac{4}{5}\right) \\ k&=\square \end{align*}
(
k
3
)
k
=
(
5
4
)
=
□
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Solve the equation.
\newline
2
3
p
=
5
p
=
□
\begin{align*} \frac{2}{3}p &= 5\\ p &= \Box \end{align*}
3
2
p
p
=
5
=
□
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Graph the solution of the following system of inequalities. Find the vertex of the solution.
\newline
{
x
+
y
≤
7
3
x
−
y
≥
9
\begin{cases} x+y \leq 7 \ 3x-y \geq 9 \end{cases}
{
x
+
y
≤
7
3
x
−
y
≥
9
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Graph the solution of the following system. Find the vertices of the solution.
\newline
{
y
≤
x
x
+
y
≥
3
x
≤
7
\begin{cases} y \leq x \ x+y \geq 3 \ x \leq 7 \end{cases}
{
y
≤
x
x
+
y
≥
3
x
≤
7
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The number of people using an older version of a spreadsheet program decreases at a rate that is proportional at any time to the number of people still using the version at that time.
\newline
There were
10
10
10
,
000
000
000
people using the older version of the spreadsheet program when the new version first came out. The number of people still using the older version decreases by
20
%
20 \%
20%
every
6
6
6
months.
\newline
How many people are still using the older version of the spreadsheet program after
2
2
2
months?
\newline
Choose
1
1
1
answer:
\newline
(A)
5848
5848
5848
\newline
(B)
9283
9283
9283
\newline
(C)
10
10
10
,
627
627
627
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