Step 1) Solve the second equation for yy:
5x - y = 35x−y=3
-color(red)(3) + 5x - y + color(blue)(y) = -color(red)(3) + 3 + color(blue)(y)−3+5x−y+y=−3+3+y
-3 + 5x - 0 = 0 + color(blue)(y)−3+5x−0=0+y
-3 + 5x = y−3+5x=y
y = -3 + 5xy=−3+5x
Step 2) Substitute (-3 + 5x)(−3+5x) for yy in the first equation and solve for xx:
-9y + 2x = 2−9y+2x=2 becomes:
-9(-3 + 5x) + 2x = 2−9(−3+5x)+2x=2
(-9 xx -3) + (-9 xx 5x) + 2x = 2(−9×−3)+(−9×5x)+2x=2
27 - 45x + 2x = 227−45x+2x=2
27 + (-45 + 2)x = 227+(−45+2)x=2
27 - 43x = 227−43x=2
-color(red)(27) + 27 - 43x = -color(red)(27) + 2−27+27−43x=−27+2
0 - 43x = -250−43x=−25
-43x = -25−43x=−25
(-43x)/color(red)(-43) = (-25)/color(red)(-43)−43x−43=−25−43
(color(red)(cancel(color(black)(-43)))x)/cancel(color(red)(-43)) = 25/43
x = 25/43
Step 3) Substitute 25/43 for x in the solution to the second equation at the end of Step 1 and calculate y:
y = -3 + 5x becomes:
y = -3 + (5 xx 25/43)
y = -3 + 125/43
y = (-3 xx 43/43) + 125/43
y = -129/43 + 125/43
y = -4/43
The solution is: x = 25/43 and y = -4/43 or (25/43, -4/43)
