SOLVING LINEAR SYSTEMS BY ELIMINATION
SOLVING LINEAR SYSTEMS BY ELIMINATION
Example 1: Eliminate one of the variables by adding like terms.
a) 3x + 4y = 11 ( b) x – 5y = 23 (
-3x + 6y = 9 ( -7x + 5y = 1 (
NOTE:
Example 2: Eliminate one of the variables by subtracting like terms.
a) 4x + 3y = 10 ( b) -6x – 7y = 12 (
9x + 3y = 5 ( -6x - 2y = -5 (
NOTE:
DIFFERENT SIGNS SAME SIGNS
_____________ like terms _____________ like terms
Example 3: Eliminate one of the variables.
a) -3x + 4y = 7 ( b) 3x + 5y = 12 (
3x + y = -2 ( 7x + 5y = 8 (
Example 4: Solve the linear system of equations by elimination and check.
|5x + y = 15 ( | STEPS: |
|2x - 3y = 6 ( |Through multiplication, obtain the same number in front of one of |
| |the variables in both equations. |
| | |
| |Decide whether to add or subtract the equations. |
| |SAME SIGNS______________ |
| |DIFFERENT SIGNS _________ |
| | |
| |Eliminate one of the variables by adding or subtracting like |
| |terms. |
| | |
| |Solve for the remaining variable. |
| | |
| |Substitute the value for the first variable into one of the |
| |equations. |
| | |
| |Solve for the second variable. |
| | |
| |Conclude. |
| | |
| |Check. |
Example 5: Solve the linear system of equations by elimination.
a) 7x – 2y = -7 ( b) 2x + 3y = 9 (
8x – 3y = 7 ( 5x + 2y = -5 (
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