# How do you solve 2x-y=3 and x+2y=24 using substitution?

Mar 30, 2018

$2 x - y = 3$
$x + 2 y = 24$

Substitution is a method for solving algebraic equations by finding the value of a variable in terms of other variables and substituting that value into existing equations.
$x = 24 - 2 y$

Substituting $24 - 2 y$ for $x$ in the first equation:

$2 \left(24 - 2 y\right) - y = 3$
$48 - 4 y - y = 3$
$5 y = 48 - 3$
$5 y = 45$
$y = 9$

Substituting $9$ for $y$ in the second equation:
$x + 2 \cdot 9 = 24$
$x = 24 - 18$
$x = 6$

Mar 30, 2018

$x = 6$ and $y = 9$.

#### Explanation:

$2 x - y = 3 \text{ " " } \left(1\right)$
$x + 2 y = 24 \text{ " " } \left(2\right)$

From eqn $\left(2\right)$

$x = 24 - 2 y \text{ " " } \left(3\right)$

Sub eqn $\left(3\right)$ into eqn $\left(1\right)$

$2 \left(24 - 2 y\right) - y = 3$

$48 - 4 y - y = 3$

$45 = 5 y$

$y = 9$

Sub $y = 9$ into eqn $\left(2\right)$

$x = 24 - 2 \left(9\right)$

$x = 6$