Question

How do you determine whether a linear system has one solution, many solutions, or no solution when given `y=5x + -1` and `y=2x+2`?

Answer 1

This system has one solution since the equations represent lines of different slopes.

Explanation:

Note that both of these equations are the equations of lines in slope intercept form.

`y = mx + c`

Further note that the slopes (`m`) of the two lines are different.

So these two lines will intersect in one point, which is the solution of the system.

graph{(y-(5x-1))(y-(2x+2)) = 0 [-8.46, 11.54, -1.44, 8.56]}