Step 1) Solve the second equation for yy:
-5x - y = 14−5x−y=14
-5x - color(blue)(14) - y + color(red)(y) = 14 - color(blue)(14) + color(red)(y)−5x−14−y+y=14−14+y
-5x - 14 - 0 = 0 + y−5x−14−0=0+y
-5x - 14 = y−5x−14=y
y = -5x - 14y=−5x−14
Step 2) Substitute (-5x - 14)(−5x−14) for yy in the first equation and solve for xx:
7y - 6x - 5 = 07y−6x−5=0 becomes:
7(-5x - 14) - 6x - 5 = 07(−5x−14)−6x−5=0
-(7 xx 5x) - (7 xx 14) - 6x - 5 = 0−(7×5x)−(7×14)−6x−5=0
-35x - 98 - 6x - 5 = 0−35x−98−6x−5=0
-35x - 6x - 98 - 5 = 0−35x−6x−98−5=0
(-35 - 6)x - 103 = 0(−35−6)x−103=0
-41x - 103 = 0−41x−103=0
-41x - 103 + color(red)(103) = 0 + color(red)(103)−41x−103+103=0+103
-41x - 0 = 103−41x−0=103
-41x = 103−41x=103
(-41x)/color(red)(-41) = 103/color(red)(-41)−41x−41=103−41
(-color(red)(cancel(color(black)(41)))x)/cancel(color(red)(-41)) = -103/41
x = -103/41
Step 3) Substitute -103/41 for x in the solution to the second equation at the end of Step 1 and calculate y:
y = -5x - 14 becomes:
y = (-5 xx -103/41) - 14
y = 515/41 - (41/41 xx 14)
y = 515/41 - 574/41
y = -59/41
The Solution Is:
x = -103/41 and y = -59/41
Or
(-103/41, -59/41)
