Question

Which ordered pair is the solution to the system of equations? {x+3y=-12, y= 1/3x-6?

Answer 1

For this, I'll be using the substitution method. Since y = 1/3x - 6, replace the y variable in the first equation with 1/3x - 6 and solve for x:

$x+3(\frac{1}{3}x-6)=-12\\ x+x-18=-12\\ 2x-18=-12\\ 2x=6\\ x=3$

Now that we have the value of x, plug it into either equation to solve for y:

$3+3y=-12\\ 3y=-15\\ y=-5\\ \\ y=\frac{1}{3}*3-6\\ y=1-6\\ y=-5$

In short, the solution to this equation is (3,-5).