Step 1) Solve the second equation for yy:
-5x + y = 27−5x+y=27
color(red)(5x) - 5x + y = color(red)(5x) + 275x−5x+y=5x+27
0 + y = 5x + 270+y=5x+27
y = 5x + 27y=5x+27
Step 2) Substitute 5x + 275x+27 for yy in the first equation and solve for xx:
7x + 2y = -317x+2y=−31 becomes:
7x + 2(5x + 27) = -317x+2(5x+27)=−31
7x + (2 * 5x) + (2 * 27) = -317x+(2⋅5x)+(2⋅27)=−31
7x + 10x + 54 = -317x+10x+54=−31
17x + 54 = -3117x+54=−31
17x + 54 - color(red)(54) = -31 - color(red)(54)17x+54−54=−31−54
17x + 0 = -8517x+0=−85
17x = -8517x=−85
(17x)/color(red)(17) = -85/color(red)(17)17x17=−8517
(color(red)(cancel(color(black)(17)))x)/cancel(color(red)(17)) = -5
x = -5
Step 3) Substitute -5 for x in the solution to the second equation at the end of Step 1 and calculate y:
y = 5x + 27 becomes:
y = (5 * -5) + 27
y = -25 + 27
y = 2
The solution is: x = -5 and y = 2 or (-5, 2)
