# How do you solve the system of equations below and give your answer as an ordered pair: 4x + 7y = 47 and 5x - 4y= -5?

Jan 16, 2018

(3,5)

#### Explanation:

$5 x - 4 y = - 5$

$5 x = 4 y - 5$

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

So we can substitute that into the equation $4 x + 7 y = 47$ to get:

$4 \left(\frac{4 y}{5} - 1\right) + 7 y = 47$

$\frac{16 y}{5} - 4 + 7 y = 47$

$\frac{16 y}{5} + 7 y = 51$

$\frac{16 y}{5} + \frac{35 y}{5} = 51$

$\frac{51 y}{5} = 51$

$51 y = 255$

$y = 5$

By plugging y back into either of the original equations, we can solve for x:

$5 x - 4 \left(5\right) = - 5$

$5 x - 20 = - 5$

$5 x = 15$

$x = 3$

Now that you have x and y, you would write out the ordered pair in the form (x,y): (3,5)