# Question #b8d66

Feb 6, 2018

$y = 4$

$x = 2$

#### Explanation:

If $4 x - 2 y = 0$ and $4 x + y = 12$, then:

$4 x - 4 x + y - \left(- 2 y\right) = 12 - 0$

$\implies 0 x + y + 2 y = 12$

$\implies 3 y = 12$

$\implies y = 4$

Since

$4 x + y = 12$

we get that

$4 x + 4 = 12$

$\implies 4 x = 12 - 4$

$\implies 4 x = 8$

$\implies x = 2$

So $y = 4$ and $x = 2$.

Feb 6, 2018

$x = 2 \mathmr{and} y = 4$

#### Explanation:

Notice that the $x$ terms are exact;y the same in both equations.

If you subtract the equations, the $x$ terms will be eliminated and you will be able to solve for $y$

$\text{ "4x +y =12" } \rightarrow A$
$\text{ "4x -2y =0" } \rightarrow B$

$A - B : \text{ " 0x+3y =12" } \rightarrow C$

$\textcolor{w h i t e}{w w w w w w w w w w w} y = 4$

Once you know the value for $y$ you can use it to find $x$

Substitute $4 \text{ for " y " in } A$

$\text{ "4x +y =12" } \rightarrow A$
$\text{ } 4 x + \left(4\right) = 12$

$\text{ } 4 x = 8$
$\text{ } x = 2$

Check in $B$

$\text{ "4x -2y =0" } \rightarrow B$
$\text{ } 4 \left(2\right) - 2 \left(4\right) = 0$
$\text{ } 8 - 8 = 0$