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When both linear equations
of a system are in the form
Ax + By = C, you can solve
the system using
elimination. You can add or
subtract equations to
eliminate a variable.
Solve the system using elimination.
5x – 6y = -32
3x + 6y = 48
First, eliminate one variable.
5x – 6y = -32
Then, find the value of the eliminated
variable by plugging x into one of the
equations.
5x – 6y = -32
5(2) – 6y = -32
10 – 6y = -32
3x + 6y = 48
8x + 0y = 16
x=2
- 6y = -42
y =7
Since x = 2 and y = 7, the solution is
(2,7).
See if (2,7) makes the other equation true.
3x + 6y = 48
3(2) + 6(7) = 48
6 + 42 = 48
48 = 48
Solve the system using elimination.
x + y = 12
x–y=2
First, eliminate one variable.
x + y = 12
Then, find the value of the eliminated
variable by plugging x into one of the
equations.
x + y = 12
(7) + y = 12
y =5
x-y= 2
2x + 0y = 14
x=7
Since x = 7 and y = 5, the solution is
(7,5).
See if (7,5) makes the other equation true.
x-y=2
(7) - (5) = 2
2=2
Solve the system using elimination.
-x + 2y = -1
x – 3y = -1
First, eliminate one variable.
-x + 2y = -1
x – 3y = -1
Then, find the value of the eliminated
variable by plugging y into one of the
equations.
-x + 2(2) = -1
-x + 4 = -1
-x = -5
x=5
0x – y = -2
y=2
Since x = 5 and y = 2, the solution is
(5,2).
See if (5,2) makes the other equation true.
x – 3y = -1
(5) – 3(2) = -1
5 – 6 = -1
-1 = -1
Solve the system using elimination.
3x + y = 8
x – y = -12
First, eliminate one variable.
3x + y = 8
x - y = -12
4x + 0y = -4
x = -1
Then, find the value of the eliminated
variable by plugging x into one of the
equations.
3x + y = 8
3(-1) + y = 8
-3 + y = 8
y = 11
Since x = -1 and y = 11, the solution is
(-1,11).
See if (-1,11) makes the other equation true.
x - y = -12
(-1) – (11) = -12
-12 = -12
Solve the system using elimination.
x + 4y = 1
3x + 12y = 3
First, eliminate one variable.
-3( x + 4y)= (1 ) -3 Multiply by -3
3x + 12y = 3
-3x – 12y = -3
3x + 12y = 3
0x + 0y = 0
0 = 0 TRUE!
Since 0 = 0 is a true
statement, there are
infinitely many solutions.
Solve the system using elimination.
3x + 4y = -10
5x – 2y = 18
First, eliminate one variable.
3x + 4y = -10
2( 5x – 2y) = (18 ) 2
Multiply by 2
Then, find the value of the eliminated
variable by plugging x into one of the
equations.
3x + 4y = -10
3(2) + 4y = -10
6 + 4y = -10
4y = -16
y = -4
3x + 4y = -10
10x – 4y = 36
13x + 0y = 26
x=2
Since x = 2 and y = -4, the solution is (2,-4).
See if (2,-4) makes the other equation true.
5x – 2y = 18
5(2) – 2(-4) = 18
10 + 8 = 18
18 = 18
Solve the system using elimination.
2x – y = 6
-3x + 4y = 1
First, eliminate one variable.
4( 2x – y )= (6 ) 4
-3x + 4y = 1
Multiply by 4
Then, find the value of the eliminated
variable by plugging x into one of the
equations.
2x – y = 6
2(5) - y = 6
10 - y = 6
-y = -4
y =4
8x – 4y = 24
-3x + 4y = 1
5x + 0y = 25
x=5
Since x = 5 and y = 4, the solution is
(5,4).
See if (5,4) makes the other equation true.
-3x + 4y = 1
-3(5) + 4(4) = 1
-15 + 16 = 1
1=1
Solve the system using elimination.
4x – 2y = 6
-2x + y = -3
First, eliminate one variable.
4x – 2y = 6
2( -2x + y)= (-3 ) 2
Multiply by 2
4x – 2y = 6
-4x + 2y = -6
0x + 0y = 0
0 = 0 TRUE!
Since 0 = 0 is a true
statement, there are
infinitely many solutions.
Solve the system using elimination.
2x – 3y = 4
3x + 2y = 6
First, eliminate one variable.
2(2x – 3y)= (4 ) 2
3( 3x + 2y) =(6 ) 3
Multiply by 2
Multiply by 3
Then, find the value of the eliminated
variable by plugging x into one of the
equations.
4x – 6y = 8
9x + 6y = 18
13x + 0y = 26
x=2
Since x = 2 and y = 0, the solution is
2x – 3y = 4
2(2) + 3y = 4
4 + 3y = 4
3y = 0
y =0
(2,0).
See if (2,0) makes the other equation true.
3x + 2y = 6
3(2) + 2(0) = 6
6+0=6
6=6
Solve the system using elimination.
x – 3y = 2
-2x + 6y = 4
First, eliminate one variable.
2(x – 3y)= (2) 2
-2x + 6y = 4
Multiply by 2
2x – 6y = 4
-2x + 6y = 4
0x + 0y = 8
0 = 8 FALSE!
Since 0 = 8 is a false
statement, there is
no solution.
Solve the system using elimination.
x+y=6
x + 3y = 10
First, eliminate one variable.
-1( x + y)= (6 ) -1
x + 3y = 10
Multiply by -1
Then, find the value of the eliminated
variable by plugging y into one of the
equations.
x+y=6
x + (2) = 6
x =4
-x - y = -6
x + 3y = 10
0x + 2y = 4
y=2
Since x = 4 and y = 2, the solution is
(4,2).
See if (4,2) makes the other equation true.
x + 3y = 10
(4) + 3(2) = 10
4 + 6 = 10
10 = 10
Solve the system using elimination.
5x + 7y = -1
4x – 2y = 22
First, eliminate one variable.
2(5x + 7y)= (-1) 2 Multiply by 2
7(4x – 2y)= (22 ) 7 Multiply by 7
Then, find the value of the eliminated
variable by plugging x into one of the
equations.
5x + 7y = -1
5(4) + 7y = -1
20 + 7y = -1
7y = -21
y = -3
10x + 14y = -2
28x – 14y = 154
38x + 0y = 152
x=4
Since x = 4 and y = -3, the solution is (4,-3).
See if (4,-3) makes the other equation true.
4x - 2y = 22
4(4) – 2(-3) = 22
16 + 6 = 22
22 = 22
Solve the system using elimination.
2x – 3y = 6
6x – 9y = 9
First, eliminate one variable.
-3(2x – 3y)= (6 ) -3
6x – 9y = 9
Multiply by -3
-6x + 9y = -18
6x – 9y = 9
0x + 0y = -9
0 = -9 FALSE!
Since 0 = -9 is a false
statement, there is
no solution.
1. 2x – 3y = 5
x + 2y = -1
5. 2x + 5y = 20
3x – 10y = 37
2. x + y = 10
x–y= 2
6. 3x + 2y = -19
x – 12y = 19
3. -x + 4y = 12
2x – 3y = 6
7. -2x + y = -1
6x – 3y = 3
4. 4x + 2y = 1
2x + y = 4
8. 4x + y = 8
-3x – y = 0