# How do you solve x + y = 3  and 3x + 4y = 8 using substitution?

Dec 6, 2016

$x = 4$ and $y = - 1$

#### Explanation:

Step 1) Solve the first equation for $y$:

$x - x + y = 3 - x$

$y = 3 - x$

Step 2) Substitute $3 - x$ for $y$ in the second equation and solve for $x$:

$3 x + 4 \left(3 - x\right) = 8$

$3 x + 12 - 4 x = 8$

$12 - x = 8$

$12 - 8 - x + x = 8 - 8 + x$

$4 = x$

$x = 4$

Step 3) substitute $4$ for $x$ in the solution to the first equation in Step 1) and calculate $y$:

$y = 3 - 4$

$y = - 1$