# How do solve the following linear system?:  5x+2y=1 , 5x-4y=23 ?

Aug 3, 2017

See below

#### Explanation:

Basically, You use both equations to find the value of one variable and plug that into one of the equations given to get the value of the other variable.

$5 x + 2 y = 1 , 5 x - 4 y = 23$

Solve equation 1 for $5 x$:

$5 x = 1 - 2 y$

Substitute into second equation:

$1 - 2 y - 4 y = 23$

Solve for $y$

-6y=22 => color(blue)(y=-22/6=-11/3

Then use the value of $y$ and substitute it into one of the equations and solve for $x$:

$5 x + 2 y = 1$

$5 x + 2 \left(- \frac{11}{3}\right) = 1$

$5 x - \frac{22}{3} = 1$

5x=25/3=>color(blue)(x=5/3

Check by graphing (the circle shows the plotted point $\left(\frac{5}{3} , - \frac{11}{3}\right)$

graph{(5x+2y-1)(5x-4y-23)((x-5/3)^2+(y+11/3)^2-.1)=0}