# How do you solve the system -4x+ y =6 and -5x - y =21 by substitution?

May 21, 2015
May 21, 2015

$- 4 x + y = 6$ ----------(1)
$- 5 x - y = 21$----------(2)

We can transpose $- 4 x$ in the first equation to the right hand side:

$y = 4 x + 6$ ------(3)

Substituting $y$ from the third equation into the second one gives us:

$- 5 x - \left(4 x + 6\right) = 21$

$- 5 x - 4 x - 6 = 21$

$- 9 x - 6 = 21$

$- 9 x = 21 + 6$

$- 9 x = 27$

Dividing both sides by $- 9$ will give us:

$\frac{\cancel{- 9} x}{\cancel{- 9}} = \frac{27}{-} 9$

color(green)(x = -3

Substituting $x = - 3$ in the third equation will give us :

$y = 4 \left(- 3\right) + 6$

$y = - 12 + 6$

 color(green)( y = -6

The solution to both these equations :x = -3; y = -6

Verify :

Substitute the values of $x \mathmr{and} y$ in both the equations to see if they are satisfied