# How do you solve the equations 8x + 3y = 16 and 2x + y = 4?

Apr 16, 2018

$x = 2$, $y = 0$

#### Explanation:

There are different methods to solve these equations.

Solving using the Elimination method

Consider the given equations:

$8 x + 3 y = 16$ . . . . . (1)
$2 x + y = 4$ . . . . . (2)

In order to make the coefficients of the variable 'y' the same, multiply equation (2) with 3.

Then,
$6 x + 3 y = 12$ . . . . . (3)

Now, in order to eliminate the variable 'y', subtract (3) from (1).

Then we get,
$2 x + 0 y = 4$

That is,
$2 x = 4$
$x = \frac{4}{2}$
$x = 2$

Now, substitute this value in (2).

Then,
$2 \left(2\right) + y = 4$
$4 + y = 4$
$y = 4 - 4$
$y = 0$