# How do you solve the following system?:  7x +5y =-15 , -4x -9y = 5

Oct 16, 2016

$x = - 2 \frac{24}{43} , \text{ } y = \frac{25}{43}$

#### Explanation:

There is no single variable, so using the method of substitution will lead to some uncomfortable math.

Let's use the elimination method.

$\textcolor{w h i t e}{\times \times \times \times x} 7 x + 5 y = - 15$...........................A
$\textcolor{w h i t e}{\times \times \times x} - 4 x - 9 y = + 5$..............................B

Make additive inverses. I have chosen the x terms for this.

$A \times 4 \text{ } 28 x + 20 y = - 60$........................C
$B \times 7 \text{ } - 28 x - 63 y = + 35$........................D

$C + D \text{ } - 43 y = - 25$

$\textcolor{w h i t e}{\times \times \times \times \times \times \times x} y = \frac{25}{43}$

Substitute $y = \frac{25}{43}$ in A

$7 x + 5 \times \left(\frac{25}{43}\right) = - 15$

$7 x = - 15 - \frac{125}{43}$

$7 x = - 17 \frac{39}{43}$

$x = - 2 \frac{24}{43}$

Substituting for x and y in B gives 5.

Despite the awkward fractions, the method remains the same.