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

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Answer 1 · 2016-08-28T21:12:24

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

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

$y = m x + c$ $y = mx + c$

Further note that the slopes ( $m$ $m$ ) 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]}

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