Question

Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically.

Answer 1

First, rewrite the equations in the form y=max + b, then graph.

You can see the graphs intersect once, so there is one solution. Estimate this solution to be at (-2,0).

Then, plug in this point into the two equations (when they are equal to each other) to see if it works.

Both sides equal to zero, so there is one solution where x = -2, y= 0 (-2, 0)

Answer 2

Answer: Infinite solutions.

Explanation:

To graph both these equations, you need to make them slope intercept form (which is y = mx + b):

x + 2y = -2 in slope intercept form is y = -1/2x - 1 (subtract x from both sides then divide both sides by 2).

-3x - 6y = 6 in slope intercept form is y = -1/2x - 1. (add 3x to both sides then divide both sides by -6).

These are the same lines, so there are an infinite number of solutions when you graph.

Hope this helps!