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

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Answer 1 · 2018-01-16T22:29:32

(3,5)

$5 x - 4 y = - 5$ $5x - 4y = -5$

$5 x = 4 y - 5$ $5x = 4y - 5$

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

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

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

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

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

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

$\frac{51 y}{5} = 51$ $(51y)/5 = 51$

$51 y = 255$ $51y = 255$

$y = 5$ $y = 5$

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

$5 x - 4 (5) = - 5$ $5x - 4(5) = -5$

$5 x - 20 = - 5$ $5x - 20 = -5$

$5 x = 15$ $5x = 15$

$x = 3$ $x = 3$

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