# How do you solve 2x-3y=1 and 5x+4y=14 using substitution?

Jun 30, 2018

$x = 2 , y = 1$

#### Explanation:

solving the first equation for $x$:
substracting $3 y$

$2 x = 1 + 3 y$
dividing by $2$ we get
$x = \frac{1}{2} + \frac{3}{2} y$
plugging this in the second equation

$5 \left(\frac{1}{2} + \frac{3}{2} y\right) + 4 y = 14$

multiplying by $2$

$5 \left(1 + 3 y\right) + 8 y = 28$
$5 + 15 y + 8 y = 28$

collecting like Terms

$23 y + 5 = 28$

substracting $5$ and dividing by $23$

$y = 1$

so we get

$x = \frac{1}{2} + \frac{3}{2} = \frac{4}{2} = 2$