# How do you find the solution of the system of equations x-4y=6 and 3x+4y=10?

Apr 26, 2018

$x = 4$
$y = - 0.5$

#### Explanation:

Because that we have one single x in one of the terms, I'm going to use the substitution method.

Given that:

$x - 4 y = 6$
$3 x + 4 y = 10$

We can rewrite the first term to get what x equals to:

$x - 4 y = 6 \implies \textcolor{g r e e n}{x = 6 + 4 y}$

Now put that in the other system to get:

$3 x + 4 y = 10 \implies 3 \left(\textcolor{g r e e n}{6 + 4 y}\right) + 4 y = 10$

And now simplify and collect terms:

$\left(3 \times 6\right) + \left(3 \times 4 y\right) + 4 y = 10$

$18 + 12 y + 4 y = 10$

$18 + 16 y = 10$

$16 y = - 8$

Now divide 16 on both sides to get y:

$\frac{16 y}{\textcolor{b l u e}{16}} = - \frac{8}{\textcolor{b l u e}{16}}$

$y = - 0.5$

Now put that into one of the two systems to get x.

$x - 4 y = 6 \implies x - 4 \textcolor{g r e e n}{\left(- 0.5\right)} = 6$

$x \textcolor{g r e e n}{+ 2} = 6$

$x = 4$

$3 x + 4 y = 10 \implies 3 \textcolor{g r e e n}{\left(4\right)} + 4 \textcolor{g r e e n}{\left(- 0.5\right)} = 10$
$12 - 2 = 10$ color(green)sqrt