5x-3y=17 and -4x+8y=20

Question

These are two problems that my daughter is having trouble figuring out.  

Answer 1

this is a system of simultaneous linear equations

5x-3y=17

-4x+8y=20

multiply the first equation by 4 and multiply the second equation by 5

4(5x)-4(3y)=4(17)

5(-4x)+5(8y)=5(20)

20x-12y=68

-20x+40y=100

add the equations to eliminate one variable, the "x"

20x+(-20x)=0

40y+(-12y)=28y

100+68=168

28y=168

y=168/28

y=6

substitute 6 for y in either original equation

5x-3(6)=17

5x-18=17

5x=17+18

5x=35

x=35/5

x=7

solution is (7,6)