# 6.2 Solve a System by Using Linear Combinations

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6.2 Solve a System by Using Linear Combinations
Secondary One 6.2 Solve a System by Using Linear Combinations

Linear Combination AKA – Elimination: Obtained by adding one of the equations (or a multiple of one of the equations) to the other equation.

How to solve a system by using Linear Combination
1. arrange the equations in standard form 2. make sure one of the variables contains an opposite coefficient. If not, make one opposites but multiplying one or both equations. 3. Add the equations vertically combining like terms 4. Solve for remaining variable 5. Substitute solution in step 4 into either equation and solve for remaining variable 6. Check solution by plugging it in.

Solve by Linear Combination
4x + 3y = 16 2x – 3y = 8

Solve by Linear Combination
-x + 2y = -8 x + 6y = -16

Solve by Linear Combination
8x – 4y = -4 4y = 3x + 14

Solve by Linear Combination
4x + 3y = 2 5x + 3y = -2

Solve by Linear Combination
3x + y = 24 7x – 3y = 8

Solve by Linear Combination
x + y = 1 5x + 4y = 14

Solve by Linear Combination
y + 3x = 2 2y + 6x = 10

Solve by Linear Combination
2y + 3x = 7 4y + 6x = 14

Solve by Linear Combination
-3x – 4y = 27 5x – 6y = -7

Assignment 6.2 Assignment