# How do you solve the system of equations 4x - 5y = 25 and  - 7x + 3y = 8?

##### 1 Answer
Feb 13, 2018

$x = - 5 \mathmr{and} y = - 9$

#### Explanation:

$4 x - 5 y = 25$------------(1)

$- 7 x + 3 y = 8$ -----------(2)

First eliminate any one variable (say $y$),

$\left(1\right) \times 3 + \left(2\right) \times 5 \implies$

$\implies 12 x - 15 y - 35 x + 15 y = 75 + 40$

$\implies 12 x - 35 x - \cancel{15 y} + \cancel{15 y} = 115$

$\implies - 23 x = 115$

$\implies x = - 5$

Substitute this value of $x$ in any one equation.

(1) $\implies 4 \times \left(- 5\right) - 5 y = 25$

$\implies - 20 - 5 y = 25$

$\implies y = \frac{25 + 20}{-} 5$

$y = - 9$

So, $x = - 5 \mathmr{and} y = - 9$

Verify by substituting both values in equation (2):

Left hand side of equation = $- 7 x + 3 y$

$\implies - 7 \times \left(- 5\right) + 3 \times \left(- 9\right) = 35 - 27 = 8$= Right hand side.

Hence verified.