I'm a parent and I'm trying to assist my son with hi math homework.. Well make sure its done properly

Question

I know the equation 2x+2y=43 & 2x+2y=30 now I have to make sure that he sets these equations using graphing substitution and elimination.

Answer 1

2x + 4y = 43

2x + 2y = 30 subtract to eliminate the x terms, and get

2y = 13

y = 13/2 or 6 1/2

plug that back into the 2nd equation

2x + 13 = 30

2x = 30-13 = 17

x = 17/2 or 8 1/2

check the answer by plugging those values back into the 1st equation

2x+ 4y = 43

17 + 4(13/2) = 43

17 +26 = 43

43 = 43

graphically, they're both downward sloping lines. 1st has slope -1/2, 2nd's slope = -1

1st has y intercept 43/4, 2nd has y intercept 15

solve each for y and then the equations are in slope intercept form: y=mx+b where m=slope and b=y intercept. y intercept of the 1st is (0,43/4) y intercept of the 2nd is (0,15)

solve the equations for x after setting y=0 and you can calculate the x intercepts, where the lines cross the x axis. 1st has x intercept (43/2,0);

2nd has x intercept (15,0)

plot the x and y intercepts. connect them with a straight line, where the 2 lines intersect is the solution, the point (8 1/2, 6 1/2) or (17/2, 13/2)