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

Mar 13, 2016

$\left(x , y\right) = \left(19 , 7\right)$

#### Explanation:

Solve by elimination and substitution

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

2)color(blue)(x-3y=-2

If you see carefully, you could eliminate $- 2 x$ from the first equation by $x$ in the second equation if we multiply $x$ with $2$ to get $2 x$

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

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

$\rightarrow 2 x - 6 y = - 4$

Now, add both of the equations

$\rightarrow \left(- 2 x + 5 y = - 3\right) + \left(2 x - 6 y = - 4\right)$

$\rightarrow - y = - 7$

rArrcolor(green)(y=7

Substitute the value of $y$ to the first equation

$\rightarrow - 2 x + 5 \left(7\right) = - 3$

$\rightarrow - 2 x + 35 = - 3$

$\rightarrow - 2 x = - 3 - 35$

$\rightarrow - 2 x = - 38$

rArrcolor(green)(x=(-38)/-2=38/2=19

Check (Substitute the values of $x$ and $y$ to the first equation)

color(orange)(-2(19)+5(7)=-3

color(orange)(-38+35=-3

color(orange)(-3=-3 =) correct!

Now to the second equation

color(indigo)(19-3(7)=-2

color(indigo)(19-21=-2

color(indigo)(-2=-2 :) correct!

$\therefore$ $x \mathmr{and} y$ have values of $19 \mathmr{and} 7$