# How do you solve the system of linear equations 2x + y = 5 and x − 2y = 10?

Apr 3, 2016

$x = 4$
$y = - 3$

#### Explanation:

first of all make any variable of the any equation the same so we will here take x and the second equation
$2 \left(x - 2 y = 10\right)$ this will make both the x values same
$2 x - 4 y = 20$ now change the signs of the second equation
so this will give us $- 2 x + 4 y = - 20$
now write both the equations simultaneously and solve them
$- 2 x \mathmr{and} + 2 x$ will be cancelled $+ y + 4 y = 5 y$ and $5 - 20 = - 15$
so $y = - 3$ Then after getting the value of y put in equation 1 and
solve it $2 x + \left(- 3\right) = 5$
$2 x = 5 + 3$
$2 x = 8$
$x = 4$