How do you solve 3x+4y=-11 and 7x-5y=3 using substitution?

Jul 17, 2016

You eliminate one variable (say $y$), ending up with an equation for only$x$, leading to the solution $x = - 1 , y = - 2$

Explanation:

You start by rewriting the first equation as

$y = - \frac{1}{4} \left(3 x + 11\right)$

Substituting this in the second equation gives

$7 x + \frac{5}{4} \left(3 x + 11\right) = 3$

or

$28 x + 15 x + 55 = 12$

Thus $43 x = - 43$, leading to $x = - 1$., and

$y = - \frac{1}{4} \left(3 \times \left(- 1\right) + 11\right) = - 2$