# How do you solve 3x+y=16 & 2x-3y=-4 using substitution?

Sep 5, 2016

$x = 4 , y = 4$

#### Explanation:

We have: $3 x + y = 16$ and $2 x - 3 y = - 4$

Let's solve the first equation for $y$:

$\implies y = 16 - 3 x$

Then, let's substitute this value of $y$ into the second equation:

$\implies 2 x - 3 \left(16 - 3 x\right) = - 4$

$\implies 2 x - 48 + 9 x = - 4$

$\implies 11 x = 44$

$\implies x = 4$

Now, let's substitute this value of $x$ into the equation for $y$:

$\implies y = 16 - 3 \left(4\right)$

$\implies y = 16 - 12$

$\implies y = 4$

Therefore, the solutions to the system of equations is $x = 4$ and $y = 4$.