Question

Which statement about this system of equations is true? A. The system has no solution. B. The system has a unique solution at (0,6). C. The system has a unique solution at (0,-4). D. The system has infinitely many solutions.

Answer 1

Answer:

A. The system has no solutions

Step-by-step explanation:

Step 1: Check to see if the 2 lines share 1 slope

slope of blue line = $\frac{y2-y1}{x2-x1} =\frac{7-6}{3-0}=\frac{1}{3}$

slope of red line = $\frac{y2-y1}{x2-x1} =\frac{-3-(-4)}{3-0}=\frac{1}{3}$

Step 2: Realize that lines with the same slope never touch

We know lines with the same slope are parallel to each other so they won't collide

Step 3: Know what the question is asking you

When they ask for solutions to the system of equations they are asking you to find out where they intersect

Step 4: Find answer

Because we know this is a parallel line they will never intersect causing this system to never have an answer or solution

Therefore the answer is A. The system has no solutions

Answer 2

Answer:

$\huge \boxed{\mathrm{Option \ A}}$

Step-by-step explanation:

For the system of equations to have solutions, the two equations have to intersect on the graph.

The two lines on the graph never intersect, therefore there are no solutions for the system of equations.