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

Jul 9, 2016

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

#### Explanation:

$\text{Solve by substitution}$

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

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

$\text{As we can see,}$ $x = 4 y + 10 ,$

$\text{we can substitute it to the first equation}$

$\rightarrow 13 \left(4 y + 10\right) + 5 y = 16$

$\text{Use the distributive property -}$ color(brown)(a(b+c)=ab+ac

$\rightarrow \left(52 y + 130\right) + 5 y = 16$

$\rightarrow 52 y + 130 + 5 y = 16$

$\rightarrow 57 y + 130 = 16$

$\rightarrow 57 y = 16 - 130$

$\rightarrow 57 y = - 114$

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

$\text{Now,substitute the value of y to the second equation}$

$\rightarrow x = 4 \left(- 2\right) + 10$

$\rightarrow x = - 8 + 10$

rarrcolor(green)(x=2

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