Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.

-6x+y=3
12x-2y=-8

1 answer

A system of linear equations has no solution when the graphs are parallel.

The slopes of parallel lines are equal.

Write your equations in slope- intercept form.

- 6 x + y = 3

Add 6 x to both sides.

y = 6 x + 3

12 x - 2 y = - 8

Divide both sides by - 2

- 6 x + y = 4

Add 6 x to both sides.

y = 6 x + 4

These two lines have the same slope so they are parallel.

Your system has no solution.