# How do you solve the system x-2y=3 and 4x-8y=12 using substitution?

Jun 3, 2018

See a solution process below:

#### Explanation:

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

$x - 2 y = 3$

$x - 2 y + \textcolor{red}{2 y} = 3 + \textcolor{red}{2 y}$

$x - 0 = 3 + 2 y$

$x = 3 + 2 y$

Step 2) Substitute $\left(3 + 2 y\right)$ for $x$ in the second equation and solve for $y$:

$4 x - 8 y = 12$ becomes:

$4 \left(3 + 2 y\right) - 8 y = 12$

$\left(4 \cdot 3\right) + \left(4 \cdot 2 y\right) - 8 y = 12$

$12 + 8 y - 8 y = 12$

$12 + 0 = 12$

$12 = 12$

This indicates there is an infinite number of solutions because these lines are in fact the same line.