Solving Linear Equations

EliminationS. Calahan

Example

x + 2y = 5 -x + y = 13

Eliminate the x since the co-efficients are opposites.

x + 2y = 5 -x + y = 13

3y = 18

3y = 18 3 3 y = 6

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 = -12 x = - 7Since y = 6 and x = -7,

then the solution is (-7, 6)

Solve the system of equations.

2x – 6y = 6 2x + 3y = 24Notice 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 -9 -9 y = 2

Using one of the 2 equations solve for x

2x – 6y = 6 Remember y = 2 So, 2x – 6(2) = 6 2x – 12 = 6 +12 +12 2x = 18

2x – 12 = 6 +12 +12 2x = 18 2 2 x = 9

So the solution is

(9, 2)