Step 1) Solve the second equation for xx:
x - 5y = -9x−5y=−9
x - 5y + color(red)(5y) = -9 + color(red)(5y)x−5y+5y=−9+5y
x - 0 = -9 + 5yx−0=−9+5y
x = -9 + 5yx=−9+5y
Step 2) Substitute (-9 + 5y)(−9+5y) for xx in the first equation and solve for yy:
6x + 2y = -46x+2y=−4 becomes:
6(-9 + 5y) + 2y = -46(−9+5y)+2y=−4
(6 xx -9) + (6 xx 5y) + 2y = -4(6×−9)+(6×5y)+2y=−4
-54 + 30y + 2y = -4−54+30y+2y=−4
-54 + (30 + 2)y = -4−54+(30+2)y=−4
-54 + 32y = -4−54+32y=−4
-54 + color(red)(54) + 32y = -4 + color(red)(54)−54+54+32y=−4+54
0 + 32y = 500+32y=50
32y = 5032y=50
(32y)/color(red)(32) = 50/color(red)(32)32y32=5032
(color(red)(cancel(color(black)(32)))y)/cancel(color(red)(32)) = 25/16
y = 25/16
Step 3) Substitute 25/16 for y in the solution to the second equation at the end of Step 1 and calculate x:
x = -9 + 5y becomes:
x = -9 + (5 xx 25/16)
x = (16/16 xx -9) + 125/16
x = -144/16 + 125/16
x = -19/16
The Solution Is:
x = -19/16 and y = 25/16
Or
(-19/16, 25/16)
