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Algebra 2
Solve a system of equations using elimination
What is the result of adding these two equations?
\newline
2
x
+
3
y
=
−
5
2 x+3 y=-5
2
x
+
3
y
=
−
5
\newline
5
x
−
y
=
−
12
5 x-y=-12
5
x
−
y
=
−
12
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What is the result of adding these two equations?
\newline
6
x
+
2
y
=
−
2
3
x
−
2
y
=
−
5
\begin{array}{l} 6 x+2 y=-2 \\ 3 x-2 y=-5 \end{array}
6
x
+
2
y
=
−
2
3
x
−
2
y
=
−
5
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Solve the system of equations.
\newline
−
5
y
+
4
x
=
49
-5 y+4 x=49
−
5
y
+
4
x
=
49
\newline
7
y
+
2
x
=
−
23
7 y+2 x=-23
7
y
+
2
x
=
−
23
\newline
x
=
x=
x
=
\newline
y
=
y=
y
=
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
2
x
+
3
y
=
−
5
2
x
−
3
y
=
10
\left\{\begin{array}{l} 2 x+3 y=-5 \\ 2 x-3 y=10 \end{array}\right.
{
2
x
+
3
y
=
−
5
2
x
−
3
y
=
10
\newline
Choose
2
2
2
answers:
\newline
(A) Subtract the bottom equation from the top equation.
\newline
(B) Add the equations.
\newline
(C) Multiply the top equation by
2
2
2
, then add the equations.
Get tutor help
Solve the system of equations.
\newline
−
7
x
−
10
y
=
45
−
3
x
−
5
y
=
25
x
=
□
y
=
□
\begin{array}{l} -7 x-10 y=45 \\ -3 x-5 y=25 \\ x=\square \\ y=\square \end{array}
−
7
x
−
10
y
=
45
−
3
x
−
5
y
=
25
x
=
□
y
=
□
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
x
−
2
y
=
11
5
x
+
3
y
=
−
11
\left\{\begin{array}{l} x-2 y=11 \\ 5 x+3 y=-11 \end{array}\right.
{
x
−
2
y
=
11
5
x
+
3
y
=
−
11
\newline
Choose
1
1
1
answers:
\newline
(A) Multiply the top equation by
5
5
5
, then add the equations.
\newline
(B) Add the equations.
\newline
(C) Multiply the top equation by
−
5
-5
−
5
, then add the equations.
Get tutor help
Solve the system of equations.
\newline
4
x
−
9
y
−
2
=
0
12
x
−
5
y
+
38
=
0
x
=
□
y
=
□
\begin{array}{l} 4 x-9 y-2=0 \\ 12 x-5 y+38=0 \\ x=\square \\ y=\square \end{array}
4
x
−
9
y
−
2
=
0
12
x
−
5
y
+
38
=
0
x
=
□
y
=
□
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
8
x
+
8
y
=
2
8
x
+
5
y
=
1
\left\{\begin{array}{l} 8 x+8 y=2 \\ 8 x+5 y=1 \end{array}\right.
{
8
x
+
8
y
=
2
8
x
+
5
y
=
1
\newline
Choose
1
1
1
answers:
\newline
(A) Add the equations.
\newline
(B) Subtract the bottom equation from the top equation.
\newline
(C) Multiply the top equation by
1
2
\frac{1}{2}
2
1
, then subtract the bottom equation from the top equation.
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
−
7
x
+
2
y
=
5
3
x
−
5
y
=
−
5
\left\{\begin{array}{l} -7 x+2 y=5 \\ 3 x-5 y=-5 \end{array}\right.
{
−
7
x
+
2
y
=
5
3
x
−
5
y
=
−
5
\newline
Choose
2
2
2
answers:
\newline
(A) Multiply the top equation by
3
3
3
, multiply the bottom equation by
7
7
7
, then add the equations.
\newline
(B) Add the equations.
\newline
(C) Multiply the top equation by
5
5
5
, multiply the bottom equation by
2
2
2
, then add the equations.
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
8
x
+
5
y
=
−
7
−
7
x
+
6
y
=
−
4
\left\{\begin{array}{l} 8 x+5 y=-7 \\ -7 x+6 y=-4 \end{array}\right.
{
8
x
+
5
y
=
−
7
−
7
x
+
6
y
=
−
4
\newline
Choose
1
1
1
answers:
\newline
(A) Multiply the top equation by
6
6
6
, multiply the bottom equation by
−
5
-5
−
5
, then add the equations.
\newline
(B) Multiply the top equation by
7
7
7
, then add the equations.
\newline
(C) Multiply the bottom equation by
8
8
8
, then add the equations.
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
2
x
−
5
y
=
13
−
3
x
+
2
y
=
13
\left\{\begin{array}{l} 2 x-5 y=13 \\ -3 x+2 y=13 \end{array}\right.
{
2
x
−
5
y
=
13
−
3
x
+
2
y
=
13
\newline
Choose
1
1
1
answers:
\newline
(A) Multiply the top equation by
3
3
3
, multiply the bottom equation by
2
2
2
, then add the equations.
\newline
(B) Subtract the bottom equation from the top equation.
\newline
(C) Multiply the top equation by
2
2
2
, multiply the bottom equation by
3
3
3
, then add the equations.
Get tutor help
Solve the system of equations.
\newline
8
y
−
9
x
=
−
3
5
y
−
8
x
=
10
x
=
□
y
=
□
\begin{array}{l} 8 y-9 x=-3 \\ 5 y-8 x=10 \\ x=\square \\ y=\square \end{array}
8
y
−
9
x
=
−
3
5
y
−
8
x
=
10
x
=
□
y
=
□
Get tutor help
Solve the system of equations.
\newline
−
9
y
+
4
x
−
20
=
0
−
7
y
+
16
x
−
80
=
0
x
=
□
y
=
□
\begin{array}{l} -9 y+4 x-20=0 \\ -7 y+16 x-80=0 \\ x=\square \\ y=\square \end{array}
−
9
y
+
4
x
−
20
=
0
−
7
y
+
16
x
−
80
=
0
x
=
□
y
=
□
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
2
x
−
6
y
=
6
6
x
−
4
y
=
2
\left\{\begin{array}{l} 2 x-6 y=6 \\ 6 x-4 y=2 \end{array}\right.
{
2
x
−
6
y
=
6
6
x
−
4
y
=
2
\newline
Choose
2
2
2
answers:
\newline
(A) Multiply the top equation by
−
3
-3
−
3
, then add the equations.
\newline
(B) Multiply the bottom equation by
3
3
3
, then subtract the bottom equation from the top equation.
\newline
(C) Multiply the bottom equation by
−
3
2
-\frac{3}{2}
−
2
3
, then add the equations.
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
10
x
+
4
y
=
−
2
5
x
−
2
y
=
2
\left\{\begin{array}{l} 10 x+4 y=-2 \\ 5 x-2 y=2 \end{array}\right.
{
10
x
+
4
y
=
−
2
5
x
−
2
y
=
2
\newline
Choose
2
2
2
answers:
\newline
(A) Multiply the top equation by
1
2
\frac{1}{2}
2
1
, then add the equations.
\newline
(B) Multiply the bottom equation by
2
2
2
, then subtract the bottom equation from the top equation.
\newline
(C) Add the equations.
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
5
x
+
3
y
=
9
4
x
−
3
y
=
9
\left\{\begin{array}{l} 5 x+3 y=9 \\ 4 x-3 y=9 \end{array}\right.
{
5
x
+
3
y
=
9
4
x
−
3
y
=
9
\newline
Choose
1
1
1
answers:
\newline
(A) Subtract the bottom equation from the top equation.
\newline
(B) Subtract the top equation from the bottom equation.
\newline
(C) Add the equations.
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
2
x
+
8
y
=
−
3
3
x
+
6
y
=
−
4
\left\{\begin{array}{l} 2 x+8 y=-3 \\ 3 x+6 y=-4 \end{array}\right.
{
2
x
+
8
y
=
−
3
3
x
+
6
y
=
−
4
\newline
Choose
2
2
2
answers:
\newline
(A) Multiply the top equation by
3
3
3
, multiply the bottom equation by
−
2
-2
−
2
, then add the equations.
\newline
(B) Multiply the top equation by
3
3
3
, multiply the bottom equation by
4
4
4
, then subtract the bottom equation from the top equation.
\newline
(C) Multiply the top equation by
−
4
-4
−
4
, multiply the bottom equation by
3
3
3
, then add the equations.
Get tutor help
Which of these strategies would eliminate a variable in the system of equations?
\newline
{
−
x
+
6
y
=
8
7
x
−
y
=
−
2
\left\{\begin{array}{l} -x+6 y=8 \\ 7 x-y=-2 \end{array}\right.
{
−
x
+
6
y
=
8
7
x
−
y
=
−
2
\newline
Choose
1
1
1
answers:
\newline
(A) Add the equations.
\newline
(B) Multiply the bottom equation by
6
6
6
, then subtract the bottom equation from the top equation.
\newline
(C) Multiply the top equation by
7
7
7
, then add the equations.
Get tutor help
Solve the system of equations.
\newline
−
3
y
+
5
x
=
26
−
2
y
−
5
x
=
−
16
x
=
□
y
=
□
\begin{array}{l} -3 y+5 x=26 \\ -2 y-5 x=-16 \\ x=\square \\ y=\square \end{array}
−
3
y
+
5
x
=
26
−
2
y
−
5
x
=
−
16
x
=
□
y
=
□
Get tutor help
Solve the system of equations.
\newline
10
y
+
7
x
=
29
−
5
y
−
9
x
=
2
x
=
□
y
=
□
\begin{array}{l} 10 y+7 x=29 \\ -5 y-9 x=2 \\ x=\square \\ y=\square \end{array}
10
y
+
7
x
=
29
−
5
y
−
9
x
=
2
x
=
□
y
=
□
Get tutor help
Solve the system of equations.
\newline
10
x
−
3
y
−
81
=
0
−
5
x
−
7
y
−
19
=
0
x
=
□
y
=
□
\begin{array}{l} 10 x-3 y-81=0 \\ -5 x-7 y-19=0 \\ x=\square \\ y=\square \end{array}
10
x
−
3
y
−
81
=
0
−
5
x
−
7
y
−
19
=
0
x
=
□
y
=
□
Get tutor help
Solve the system of equations.
\newline
−
5
x
+
8
y
=
0
−
7
x
−
8
y
=
−
96
x
=
□
y
=
□
\begin{array}{l} -5 x+8 y=0 \\ -7 x-8 y=-96 \\ x=\square \\ y=\square \end{array}
−
5
x
+
8
y
=
0
−
7
x
−
8
y
=
−
96
x
=
□
y
=
□
Get tutor help
Solve the system of equations.
\newline
9
x
−
4
y
=
−
7
7
x
−
12
y
=
39
x
=
□
y
=
□
\begin{array}{l} 9 x-4 y=-7 \\ 7 x-12 y=39 \\ x=\square \\ y=\square \end{array}
9
x
−
4
y
=
−
7
7
x
−
12
y
=
39
x
=
□
y
=
□
Get tutor help
What is the result of subtracting the second equation from the first?
\newline
−
7
x
−
y
=
0
7
x
+
8
y
=
−
6
\begin{aligned} -7 x-y & =0 \\ 7 x+8 y & =-6 \end{aligned}
−
7
x
−
y
7
x
+
8
y
=
0
=
−
6
Get tutor help
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
\newline
At a community barbecue, Mrs. Callahan and Mr. Maynard are buying dinner for their families. Mrs. Callahan purchases
3
3
3
hot dog meals and
2
2
2
hamburger meals, paying a total of \(32. Mr. Maynard buys
2
2
2
hot dog meals and
1
1
1
hamburger meal, spending
19
19
19
\) in all. How much do the meals cost?
\newline
Hot dog meals cost
$
_
_
_
_
\$\_\_\_\_
$____
each, and hamburger meals cost
$
_
_
_
_
\$\_\_\_\_
$____
each.
Get tutor help
Solve using elimination.
\newline
7
x
−
8
y
=
−
17
7x - 8y = -17
7
x
−
8
y
=
−
17
\newline
−
7
x
+
3
y
=
2
-7x + 3y = 2
−
7
x
+
3
y
=
2
\newline
(
_
_
_
_
,
_
_
_
_
)
(\_\_\_\_, \_\_\_\_)
(
____
,
____
)
Get tutor help
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