Need help on how to break this down to find answer

Question

What is the x-coordinate of the point where the lines x=4y−8 and 1/2x+y=11 intersect? How do I figure this out

Answer 1

solve each equation for y, then set them equal and solve for x

x=4y-8

4y = x+8

y = x/4 +2

(1/2)x +y = 11

y = -(1/2)x + 11

set the 2 expressions for y equal to each other

x/4 +2 = (-1/2)x + 11

(1/2)x + x/4 = 11-2

3x/4 = 9

x = (4/3)(9) = 12 is the x coordinate where the lines intersect

y=-(1/2)(12) + 11 =-6+11 = 5 is the y coordinate where they intersect

(12,5) is the point where the lines intersect