How do you solve by substitution x + 3y = 5 and 4x + 5y = 13?

1 Answer
Jun 8, 2015

x+3y=5
color(blue)(x=5-3y ( we substract 3y on each side )

Now that we have color(blue)x, we can substitute it in the second equation :

4color(blue)x+5y=13
4*color(blue)((5-3y))+5y=13
20-12y+5y=13
20-7y=13
20=13+7y ( we add 7y on each side )
20-13=7y
7y=7
color(red)(y=1 ( we divide by 7 on each side )

Now that we have color(red)y, we can find color(blue)x :

color(blue)x=5-3color(red)y
color(blue)x=5-3*1
color(blue)x=5-3
color(blue)(x=2)