# How do you solve 5x+y=15, 2x+y=12 using substitution?

Dec 10, 2016

$x = 1$ and $y = 10$

#### Explanation:

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

$5 x - 5 x + y = 15 - 5 x$

$0 + y = 15 - 5 x$

$y = 15 - 5 x$

Step 2) Substitute $15 - 5 x$ for $y$ in the second equation and solve for $x$:

$2 x + \left(15 - 5 x\right) = 12$

$2 x + 15 - 5 x = 12$

$2 x + 15 - 15 - 5 x = 12 - 15$

$2 x - 5 x + 0 = - 3$

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

$- 3 x = - 3$

$\frac{- 3 x}{- 3} = \frac{- 3}{- 3}$

$\frac{- 3}{- 3} x = 1$

$1 x = 1$

$x = 1$

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

$y = 15 - 5 \cdot 1$

$y = 15 - 5$

$y = 10$