# How do you solve 2x-3y=24 and y+7x=46 using substitution?

Jul 30, 2016

$x = \frac{162}{23}$
$y = - \frac{76}{23}$

#### Explanation:

Multiplying both sides of the equation $y + 7 x = 46$ by $3$
we get
$3 y + 21 x = 138$
$2 x - 3 y = 24$
Adding up both the above equations
we get
$3 y + 21 x + 2 x - 3 y = 138 + 24$
or
$23 x = 162$
or
$x = \frac{162}{23}$
From the equation $y + 7 x = 46$
we get
$y = 46 - 7 x$
or
$y = 46 - 7 \left(\frac{162}{23}\right)$
or
$y = 46 - \frac{1134}{23}$
or
$y = \frac{46 \left(23\right) - 1134}{23}$
or
$y = \frac{1058 - 1134}{23}$
or
$y = - \frac{76}{23}$