Question

Solve each system of equations using substitution. Show all work.

1) x - y = 2
4x - 3y = 11

2) -2x + 3y = 14
x + 2y = 7

3) 6x - y = -4
2x + 2y = 15

Answer 1

first make an equaiton equal to only 1 variable 1. x-y=2 add y to both sides x=y+2 sub 4(y+2)-3y=11 4y+8-3y=11 y+8=11 y=3 sub x=y+2 x=3+2 x=5 (5,3) 2. x+2y=7 subtract 2y x=7-2y sub -2(7-2y)+3y=14 -14+4y+3y=14 7y-14=14 7y=28 y=4 sub x=7-2y x=7-2(4) x=7-8 x=-1 (-1,4) 3. 6x-y=-4 subtract 6x -y=-4-6x multily -1 y=4+6x sub 2x+2(4+6x)=15 2x+8+12x=15 14x+8=15 14x=7 x=1/2 sub y=4+6x y=4+6(1/2) y=4+3 y=7 (1/2,7) 1. (5,3) 2. (-1,4) 3. (1/2,7)