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Solving Linear EquationsElimination S. Calahan
x + 2y = 5 -x + y = 13 Example Eliminate the x since theco-efficients are opposites.
x + 2y = 5 -x + y = 13 3y = 18
3y = 18 y = 6
Use one of the original equations to substitute y =6. x + 2y = 5 y = 6, so find x Use one of the original equations to substitute y =6. x + 2y = 5 x + 2(6) = 5 x + 12 = 5
x + 12 = 5 x + 12 = 5 Solve = -12 x = - 7 Since y = 6 and x = -7, then the solution is (-7, 6)
Solve the system of equations.2x – 6y = 6 2x + 3y = 24 Notice the x co-efficients are the same.
Subtract the equations 2x – 6y = 6 - (2x + 3y = 24)Distribute the negative
Now add 2x – 6y = 6 -2x - 3y = -24 -9y = - 18 y = 2
Using one of the 2 equations solve for x2x – 6y = 6 Remember y = 2 So, 2x – 6(2) = 6 2x – 12 = 6 2x = 18
2x – 12 = 6 2x = 18 x = 9
So the solution is (9, 2)
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