# How do you solve 7/4x – 5/2y = 2 and 1/4x + 7/2y = 8?

$x = 4$
$y = 2$

#### Explanation:

From the give $\frac{7}{4} x - \frac{5}{2} y = 2$ and $\frac{1}{4} x + \frac{7}{2} y = 8$

Multiply both equations by 4 to get rid of the fractions
so that the two equations become

$7 x - 10 y = 8 \text{ " }$call this the 1st equation
$x + 14 y = 32 \text{ " }$call this the 2nd equation

Multiply again the 2nd equation by 7 to make it

$7 x + 98 y = 224$call this the new 2nd equation

We will use now the new 2nd and the 1st respectively

$7 x + 98 y = 224$
$7 x - 10 y = 8 \text{ " }$

Perform subtraction to obtain

$108 y = 216$

then $y = 2$

Solve for x now using the old second equation $x + 14 y = 32$
and $y = 2$

$x + 14 y = 32$
$x + 14 \left(2\right) = 32$
$x = 32 - 28$
$x = 4$

Our solution is $x = 4$ and $y = 2$

God bless...I hope the explanation is useful..