Answer:
Exactly one solution.
Step-by-step explanation:
We have been given a system of equations. We are asked to find the number of solutions for our given system.
[tex]y=x+2...(1)[/tex]
[tex]6x-4y=-10...(2)[/tex]
We can see that equation (1) in slope-intercept form of equation.
We will convert equation (2) in slope-intercept form of equation as shown below:
[tex]6x-6x-4y=-10-6x[/tex]
[tex]-4y=-6x-10[/tex]
Divide both sides by [tex]-4[/tex].
[tex]\frac{-4y}{-4}=\frac{-6x}{-4}+\frac{-10}{-4}[/tex]
[tex]y=\frac{3}{2}x+\frac{5}{2}[/tex]
We can see that slopes of both lines are different, therefore, our given lines will intersect exactly at one point and our given system of equations has exactly one solution.
