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

May 21, 2015

$y = 2 - x$ --------------(1)

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

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

$5 = \left(2 - x\right) + 2 x$

$5 = 2 - x + 2 x$

$5 = 2 + x$

Transposing 2 to the left hand side gives us :

$5 - 2 = x$

color(green)(x = 3

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

$y = 2 - 3$

 color(green)(y = -1

The solution to both these equations :x = 3; y = -1

Verify :

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