# How do you solve by substitution 4x + 6y = 62  and 10x - 2y = 2?

Jun 5, 2015

$10 x - 2 y = 2$
$10 x = 2 + 2 y$ ( we add $2 y$ on each side )
$10 x - 2 = 2 y$ ( we substract $2$ on each side )
$5 x - 1 = y$ ( we divide by $2$ on each side )

Now that we have $y$, we can use substitution in the first equation :

$4 x + 6 \cdot \left(5 x - 1\right) = 62$
$4 x + 30 x - 6 = 62$
$34 x - 6 = 62$
$34 x = 62 + 6$ ( we add $6$ on each side )
$34 x = 68$
$x = \frac{68}{34} = 2$ ( we divide by $34$ on each side )

Now that we have $x$, we can find $y$ :

We know that $y = 5 x - 1$, as we calculated it before :

$y = 5 \cdot 2 - 1 = 10 - 1 = 9$