How do you solve the system 13x + 5y = 16 and x = 4y + 10?

1 Answer
Jul 9, 2016

color(purple)({x,y=2,-2}

Explanation:

"Solve by substitution"

color(blue)(13x+5y=16 (1st "equation")

color(blue)(x=4y+10 (2nd "equation")

"As we can see," x=4y+10,

"we can substitute it to the first equation"

rarr13(4y+10)+5y=16

"Use the distributive property -" color(brown)(a(b+c)=ab+ac

rarr(52y+130)+5y=16

rarr52y+130+5y=16

rarr57y+130=16

rarr57y=16-130

rarr57y=-114

rarrcolor(green)(y=-144/57=-2

"Now,substitute the value of y to the second equation"

rarrx=4(-2)+10

rarrx=-8+10

rarrcolor(green)(x=2

color(purple)({x,y=2,-2}