Consider the system of equations

{ - 2x + 6y = - 8

{ cx + 3y = - 4

What value of c would produce a system that has an infinite number of solutions?

Justify your answer.

Explain why there is no value of c that would produce a system with no solution.

Enter your answer, justification, and explanation in the box provided.

Make the equation the same or a multiple of the other to have an infinite number of solutions. See how the - 8/2 = - 4 and 6/2=3? then - 2/2 = c

Make c = - 1 and they are the same linear equation. (same slope, same intercepts, same line) and therefore have infinite solutions.

In order to have no solutions, the lines cannot cross at all and so they must be parallel but not the same line. Parallel lines have the same slope with different intercepts. if you rearrange both equations in slope intercept form:

y = x/3 - 4/3

y = - cx/3 - 4/3

no matter what you make c the lines will always cross at the y-intercept (0, - 4/3). this is a solution and therefore there's no value of c that would produce a system with no solution.