Solving a System with Linear Combination

Equations:

2x-4y = 13

4x-5y = 8

1. Multiply the first equation by -2 so that the x-coefficients differ only in sign.

2x-4y = 13 ...........times -2..................-4x+8y = -26

4x-5y = 8.............................................4x-5y = 8

2. Add the equations..............................3y = -18

...............................................................y = -6

3. Substitute the value of y into one of the original equations. Solve for x.

write equation 1......................................2x-4y = 13

substitute -6 for y....................................2x-4(-6) = 13

simplify....................................................2x=24 = 13

solve for x................................................x = (-11/2,-6 )

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