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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