Question

Solving a system of equations using substitution

y=3x+3
y=2x+8

~~~~~~~~~~
x+3y=17
2x+3y=22

Answer 1

1.

`y=3x+3 \\ y=2x+8 \\ \\ \hbox{substitute 3x+3 for y in the 2nd equation:} \\ 3x+3=2x+8 \\ 3x-2x=8-3 \\ x=5 \\ \\ y=2x+8=2 * 5+8=10+8=18 \\ \\ \boxed{(x,y)=(5,18)}`

2.

`x+3y=17 \\ 2x+3y=22 \\ \\ \hbox{solve the 1st equation for x:} \\ x+3y=17 \\ x=17-3y \\ \\ \hbox{substitute 17-3y for x in the 2nd equation:} \\ 2(17-3y)+3y=22 \\ 34-6y+3y=22 \\ -6y+3y=22-34 \\ -3y=-12 \\ y=(-12)/(-3) \\ y=4 \\ \\ x=17-3y=17-3 * 4=17-12=5 \\ \\ \boxed{(x,y)=(5,4)}`