Answer:
Our given system has exactly one solution.
Step-by-step explanation:
We have been given a system of equation. We are asked to find the number of solutions for our given system.
First of all, we will convert our second equation in slope-intercept form of equation as shown below:
[tex]-8x-4y=-20[/tex]
Upon dividing both sides of our equation by -4, we will get:
[tex]\frac{-8x}{-4}-\frac{4y}{-4}=\frac{-20}{-4}[/tex]
[tex]2x+y=5[/tex]
[tex]2x-2x+y=-2x+5[/tex]
[tex]y=-2x+5[/tex]
Upon comparing our both equations, we can see that they have different slopes and different y-intercepts, therefore, they will have exactly one solutions as they will intersect at one place.
Upon looking at our attachment, we can see that our explanation is correct.
