# How do you solve the system x = y + 4 and 2x - 5y = 2 by substitution?

May 21, 2015

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

Substituting $x$ from the first equation into the second one gives us:

$2 \left(y + 4\right) - 5 y = 2$

$2 y + 8 - 5 y = 2$

$- 3 y + 8 = 2$

$- 3 y = 2 - 8$

$- 3 y = - 6$

Dividing both sides by $- 3$ will give us:

$\frac{\cancel{- 3} y}{\cancel{- 3}} = \frac{- 6}{-} 3$

color(green)(y = 2

Substituting $y = 2$ in the first equation will give us :

$x = 2 + 4$

color(green)(x = 6

The solution to both these equations :x = 6; y = 2

Verify :

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