# How do you solve the following system?: y=2x-3 , 5x + 3y = -3

Mar 14, 2016

$x , y = \frac{6}{11} , - \frac{21}{11}$

#### Explanation:

color(blue)(y=2x-3

color(blue)(5x+3y=-3

Substitute the value of $y$ to the second equation

$\rightarrow 5 x + 3 \left(2 x - 3\right) = - 3$

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

$\rightarrow 5 x + 6 x - 9 = - 3$

$\rightarrow 11 x - 9 = - 3$

$\rightarrow 11 x = - 3 + 9$

$\rightarrow 11 x = 6$

color(green)(rArrx=6/1

Substitute the value of $x$ to the first equation

$\rightarrow y = 2 \left(\frac{6}{11}\right) - 3$

$\rightarrow y = \frac{12}{11} - 3$

color(green)(rArry=-21/11#