Objective: Solve systems of linear equations
using elimination
Example 1)
3 x + 2 y = 2
-3 x + 2 y = 6
Add the equations
4 y = 8
Simplify
y = 8/4 = 2
Substitute using y = 2
3 x + 2(2) = 2
3 x + 4 = 2
Simplify
3 x = -2
x = -2/3
Solution (-2/3, 2)
Example 2)
- x - y = 8
-2 x - y = -1
Subtract the equations
x = 9
Substitute using x = 9
-9 - y = 8
- y = 17
y = -17
Solution (9, -17)
Example 3)
2 x = -3 y + 1
x + 2 y = -1
Rewrite in standard form
2 x + 3 y = 1
x + 2 y = -1
Multiply the 2nd equation by -2 then add
2 x + 3 y = 1
-2 x - 4 y = 2
Simplify
-y = 3
y = -3
Substitute using y = -3
x + 2(-3) = -1
x + -6 = -1
x = 5
Solution (5, -3)
Example 4)
3 x + 2 y = 1
2 x - 5 y = -2
Let’s eliminate the x
-2(3 x + 2 y ) = -2 (1)
3(2 x - 5 y )
= 3(-2)
Multiply the first equation
by -2
Multiply the 2nd equation by 3
-6 x - 4 y = -2
6 x - 15 y = -6
Now add.
-19 y = -8 y
Now substitute
Simplify.
Solution:
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