Their are 2 main methods of solving 2 equations with 2 variables: 1) SUBSTITUTION 2) ELIMINATION I'll show you both:
1) y = 2x + 160 y = - 3x + 208 plug what y is equal to in 1st equation into the y of the 2nd: 2x + 160 = -3x + 208 2x + 3x + 160 = -3x + 3x + 208 5x + 160 -160 = 208 - 160 5x = 48 5x/5 = 48/5 x = 48/5 = 9 3/5 now plug that x into either one of the original equations: y = -3x + 208 = -3(48/5) + 208 y = -144/5 + 208 = 1040/5 - 144/5 = 896/5 y = 179 1/5
2) add the whole equations together so as to cancel out one of the variables: I'm choosing to eliminate the y, so we need y-y to remove the y's, I'll multiply the whole 2nd equation by -1 to make that -y -1 (y = - 3x + 208) -y = 3x - 208 So set it up like: y = 2x + 160 -[y = 3x - 208] --------------------- 0 = 5x - 48 0+48 = 5x -48 +48 5x = 48 5x/5 = 48/5 x = 48/5 plug that x value into one of the original equations: y = 2x + 160 = 2(48/5) + 160 y = 96/5 + 160 = 96/5 + 800/5 = 896/5 y = 179 1/5
SO WE GOT THE SAME VALUES BOTH WAYS. WHEN YOU SEE FUTURE PROBLEMS LIKE THESE, SOME WILL BE QUICKER BY ELIMINATION AND OTHERS BY SUBSTITUTION
