Step 1) Solve the second equation for yy:
4x + y = 14x+y=1
-color(red)(4x) + 4x + y = -color(red)(4x) + 1−4x+4x+y=−4x+1
0 + y = -4x + 10+y=−4x+1
y = -4x + 1y=−4x+1
Step 2) Substitute (-4x + 1)(−4x+1) for yy in the first equation and solve for xx:
6x + 2y = -26x+2y=−2 becomes:
6x + 2(-4x + 1) = -26x+2(−4x+1)=−2
6x + (2 * -4x) + (2 * 1) = -26x+(2⋅−4x)+(2⋅1)=−2
6x + (-8x) + 2 = -26x+(−8x)+2=−2
6x - 8x + 2 = -26x−8x+2=−2
(6 - 8)x + 2 = -2(6−8)x+2=−2
-2x + 2 = -2−2x+2=−2
-2x + 2 - color(red)(2) = -2 - color(red)(2)−2x+2−2=−2−2
-2x + 0 = -4−2x+0=−4
-2x = -4−2x=−4
(-2x)/color(red)(-2) = (-4)/color(red)(-2)−2x−2=−4−2
(color(red)(cancel(color(black)(-2)))x)/cancel(color(red)(-2)) = 2
x = 2
Step 3) Substitute 2 for x in the solution to the second equation at the end of Step 1 and calculate y:
y = -4x + 1 becomes:
y = (-4 * 2) + 1
y = -8 + 1
y = -7
The solution is: x = 2 and y = -7 or (2, -7)
