Step 1) Solve the first equation for xx:
x - 7y = 9x−7y=9
x - 7y + color(red)(7y) = 9 + color(red)(7y)x−7y+7y=9+7y
x - 0 = 9 + 7yx−0=9+7y
x = 9 + 7yx=9+7y
Step 2) Substitute 9 + 7y9+7y for xx in the second equation and solve for yy:
7y = 3x + 17y=3x+1 becomes:
7y = 3(9 + 7y) + 17y=3(9+7y)+1
7y = (3 * 9) + (3 * 7y) + 17y=(3⋅9)+(3⋅7y)+1
7y = 27 + 21y + 17y=27+21y+1
7y = 28 + 21y7y=28+21y
7y - color(red)(21y) = 28 + 21y - color(red)(21y)7y−21y=28+21y−21y
(7 - color(red)(21))y = 28 + 0(7−21)y=28+0
-14y = 28−14y=28
(-14y)/color(red)(-14) = 28/color(red)(-14)−14y−14=28−14
(color(red)(cancel(color(black)(-14)))y)/cancel(color(red)(-14)) = -2
y = -2
Step 3) Substitute -2 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = 9 + 7y becomes:
x = 9 + (7 * -2)
x = 9 + (-14)
x = 9 - 14
x = -5
The solution is: x = -5 and y = -2 or (-5, -2)
