You Will Be Able To:
Solve Systems by Elimination
Solve Systems by Elimination:
1)
2)
3)
4)
5)
Put each equation in standard form
Make one variable opposite each other
Add the equations
Solve for the variable
Plug answer into any equation to find
the other variable
6) Write answer as ordered pair (x,y)
Example 1: Rewrite the linear system so that the
like terms are arranged in columns
a.
3x – y = 23
y + 8x = 11
3x – y = 23
8x + y = 11
Example 1: Rewrite the linear system so that the
like terms are arranged in columns
b.
4x = y + 1
3y + 4x = 7
4x – y = 1
4x + 3y = 7
Example 1: Rewrite the linear system so that the
like terms are arranged in columns
c.
7x – y = 13
y = 14x – 3
7x – y = 13
-14x + y = -3
Example 2: Use the linear combination method to
solve the system.
+
2x + 3y = 11
-2x + 5y = 13
8y = 24
y=3
2x + 3(3) = 11
2x + 9 = 11
2x = 2
x=1
(1, 3)
+
6x – 4y = 14
-3x + 4y = 1
= 15
3x
x=5
-3(5) + 4y = 1
-15 + 4y = 1
4y = 16
y=4
(5, 4)
+
4x – 3y = 5
–2x + 3y = -7
= -2
2x
x = -1
-2(-1) + 3y = -7
2 + 3y = -7
3y = -9
y = -3
(-1, -3)
Example 3: Use the linear combination method to solve the
system.
3x + 4y = -6
2y = 3x +6
3x + 4y = -6
+ -3x + 2y = 6
6y = 0
y=0
3x + 4(0) = -6
3x = -6
x = -2
(-2, 0)
8x – 4y = -4
4y = 3x + 14
8x – 4y = -4
+ -3x + 4y = 14
5x
= 10
x=2
-3(2) + 4y = 14
-6 + 4y = 14
4y = 20
y=5
(2, 5)
-5y = -4x – 6
2x + 5y = 12
+
4x – 5y = –6
2x + 5y = 12
6x
=6
x=1
2(1) + 5y = 12
2 + 5y = 12
5y = 10
y=2
(1, 2)
x + y = 24
x–y= 2
+
x + y = 24
x–y= 2
13 + y = 24
= 26
y = 11
2x
x = 13
11 & 13
x + y = 37
x – y = -5
+
x + y = 37
x – y = -5
16 + y = 37
= 32
y = 21
2x
x = 16
16 & 21