# If 1/4x=5-1/2y, what is the value of x+2y?

Nov 30, 2016

$x + 2 y = 20$

#### Explanation:

Simplify the given equation first by getting rid of the decimals.

$\frac{1}{4} x = 5 - \frac{1}{2} y \text{ } \leftarrow \times 4$

$4 \times \frac{1}{4} x = 4 \times 5 - 4 \times \frac{1}{2} y$

$x = 20 - 2 y \text{ } \leftarrow$ the variables are almost what we need.

Re-arranging gives exactly what we want.

$x + 2 y = 20$

Note that because there are 2 variables, there is no one unique solution to the equation, but infinitely many solutions.

(This is the equation of a straight line.)