Question

Which values of m and b will create a system of equations with no solution? Check all that apply. y = mx + b y = –2x +

Answer 1

The graph of a linear equation is a straight line.  The "solution" to a system of two linear equations is the point where the two lines cross.  If the two lines are parallel, they never cross; hence parallel lines have no solution.  Two lines are parallel if they have the same slope (the m value in y = mx+b).  One of your equations is y = -2x + (you left the y-intercept out).  The slope is -2.  So any line with a slope of m = -2 will be parallel to this line and will not cross it.  The second line also needs a different value of b, the y-intercept.  Otherwise it is the same line and every point is a solution.  So if your equation is:

 

y = -2x + 1

 

Then any equation of the form y = -2x + b, b≠1 will create a system with no solution.  Hence the values of m and b are m = -2, b ≠ 1.