Question

How many solutions does this linear system have?

y = x+ 2

6x – 4y = –10

Answer 1

no solutions

Explanation:

Answer 2

Exactly one solution.

Explanation:

We have been given a system of equations. We are asked to find the number of solutions for our given system.

`y=x+2...(1)`

`6x-4y=-10...(2)`

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:

`6x-6x-4y=-10-6x`

`-4y=-6x-10`

Divide both sides by
`-4`.

`(-4y)/(-4)=(-6x)/(-4)+(-10)/(-4)`

`y=(3)/(2)x+(5)/(2)`

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.