Question

Which value of m will create a system of parallel lines with no solution?

y=mx-6

8x-4y=12

A coordinate grid with one line labeled 8 x minus 4 y equals 12. The line passes through a point at (0, negative 3), (1, negative 1) and a point at (1.5, 0).

Answer 1

Answer:

1) First let's put both into equivalent forms by solving the second equation for y.

8x - 4y = 12

-4y = -8y + 12

y = 2y -3

We now have two equations:

y = mx - 6

y = 2x - 3

Recall that parallel lines have the same slope, and the slope is "m" for an equation in slope-intercept form y=mx+b.

The slope in y = 2x - 3 is 2, so for the equation y = mx -6 to be parallel, it must also have a slope of 2.

Therefore, m = 2.

Answer 2

   m = 2 should be the value for no solution of the system of two parallel lines.

     System of two parallel lines have been given as,

• y = mx - 6 -------- (1)
• 8x - 4y = 12 -------(2)

Condition for a system of two parallel lines with no solution,

    "Two lines with same slope but different y-intercepts"

By solving equation (2),

8x - 4y = 12

2x - y = 3

y = 2x - 3

Since, this equation is parallel to equation (1), slopes of both the lines will be equal.

     Therefore, m = 2 will be the value of the slope.

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