How do you solve 4x+y=-5 and 2x+3y=5 using substitution?

May 25, 2018

$x = - 2$
$y = 3$

Explanation:

$4 x + y = - 5$
$2 x + 3 y = 5$

Rearrange the first equation for $y$:

$4 x + y = - 5$

$y = - 5 - 4 x$

Substitute $y$ into second equation and solve for $x$:

$2 x + 3 y = 5$

$2 x + 3 \left(- 5 - 4 x\right) = 5$

$2 x - 15 - 12 x = 5$

$2 x - 12 x = 5 + 15$

$- 10 x = 20$

$x = \frac{20}{-} 10$

$x = - 2$

Then substitute the value of $x$ into one of the original equations to find the solution for $y$:

$4 x + y = - 5$

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

$- 8 + y = - 5$

$y = - 5 + 8$

$y = 3$

Double check your solution by substituting values of $x = - 2$ and $y = 3$ into any of the original equations and see whether you get the numerical solution ($- 5$ or $5$).