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Let’s check out your problem:
Solve the
system of equations
using elimination:
2
x
+
3
y
=
−
14
2 x+3 y=-14
2
x
+
3
y
=
−
14
and
x
+
5
y
=
0
x+5 y=0
x
+
5
y
=
0
.
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Home
Math Problems
Algebra 2
Solve a system of equations in three variables using elimination
Full solution
Q.
Solve the system of equations using elimination:
2
x
+
3
y
=
−
14
2 x+3 y=-14
2
x
+
3
y
=
−
14
and
x
+
5
y
=
0
x+5 y=0
x
+
5
y
=
0
.
Write Equations:
Write down the system of equations.
\newline
2
x
+
3
y
=
−
14
2x + 3y = -14
2
x
+
3
y
=
−
14
\newline
x
+
5
y
=
0
x + 5y = 0
x
+
5
y
=
0
Multiply and Set Up:
Multiply the second equation by
−
2
-2
−
2
to set up for elimination of
x
x
x
.
−
2
(
x
+
5
y
)
=
−
2
(
0
)
-2(x + 5y) = -2(0)
−
2
(
x
+
5
y
)
=
−
2
(
0
)
−
2
x
−
10
y
=
0
-2x - 10y = 0
−
2
x
−
10
y
=
0
Eliminate x:
Add the modified second equation to the first equation to eliminate x.
\newline
(
2
x
+
3
y
)
+
(
−
2
x
−
10
y
)
=
−
14
+
0
(2x + 3y) + (-2x - 10y) = -14 + 0
(
2
x
+
3
y
)
+
(
−
2
x
−
10
y
)
=
−
14
+
0
\newline
2
x
−
2
x
+
3
y
−
10
y
=
−
14
2x - 2x + 3y - 10y = -14
2
x
−
2
x
+
3
y
−
10
y
=
−
14
\newline
0
x
−
7
y
=
−
14
0x - 7y = -14
0
x
−
7
y
=
−
14
Solve for y:
Solve for y.
\newline
−
7
y
=
−
14
-7y = -14
−
7
y
=
−
14
\newline
y
=
−
14
−
7
y = \frac{-14}{-7}
y
=
−
7
−
14
\newline
y
=
2
y = 2
y
=
2
Substitute and Find
x
x
x
:
Substitute
y
=
2
y = 2
y
=
2
into the second original equation to find
x
x
x
.
x
+
5
(
2
)
=
0
x + 5(2) = 0
x
+
5
(
2
)
=
0
x
+
10
=
0
x + 10 = 0
x
+
10
=
0
x
=
−
10
x = -10
x
=
−
10
Write Ordered Pair:
Write the solution as an ordered pair
(
x
,
y
)
(x, y)
(
x
,
y
)
.
\newline
The solution is
(
−
10
,
2
)
(-10, 2)
(
−
10
,
2
)
.
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Anna does sit-ups to get ready for her first triathlon. When she starts, she does a sit-up every
2
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\newline
Is the number of sit-ups Anna does proportional to the time she spends doing them?
\newline
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\newline
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y
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\newline
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\newline
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Question
What is the result of subtracting the second equation from the first?
\newline
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x
+
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=
0
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2
x
+
y
=
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\newline
−
7
x
+
3
y
=
2
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−
7
x
+
3
y
=
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\newline
□
\square
□
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Question
What is the result of subtracting the second equation from the first?
\newline
2
x
+
7
y
=
−
8
2
x
−
5
y
=
−
1
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2
x
+
7
y
=
−
8
2
x
−
5
y
=
−
1
\newline
□
\square
□
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Question
What is the result of adding these two equations?
\newline
5
x
−
y
=
6
5 x-y=6
5
x
−
y
=
6
\newline
−
2
x
+
y
=
8
-2 x+y=8
−
2
x
+
y
=
8
\newline
□
\square
□
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Question
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(A) Yes
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(B) No
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m
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\newline
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Could
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c
m
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cm
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\newline
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1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
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Could
10.5
c
m
,
8.0
c
m
10.5 \mathrm{~cm}, 8.0 \mathrm{~cm}
10.5
cm
,
8.0
cm
, and
4.0
c
m
4.0 \mathrm{~cm}
4.0
cm
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\newline
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