Question

Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution.

Answer 1

First, get one of the variables on its own. I'm going to do the first equation since it looks easier. :)

$3x + 6y = 18$
Subtract 6y from both sides.

$3x = 18 - 6y$
Divide both sides by 3 to get the variable alone.
$x = 6 - 2y$
Plug this into the other equation for x.

$3y = - \frac{3}{2} (6 - 2y) + 9$
Distribute.

$3y = - 9 + 3y + 9$
Add like terms.

$3y = 3y$
The system has infinitely many solutions because both sides equal each other.

Hope this helped!

:)