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Verified Answer :

nobrains

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.

The value of \(m\) is \(2\).

Given:

The given equations are:

\(y=mx-6\)        ...(i)

\(8x-4y=12\)         ...(ii)

To find:

The value of \(m\) that will create a system of parallel lines with no solution.

Explanation:

The slope-intercept form of a line is:

\(y=mx+b\)           ...(iii)

where, \(m\) is the slope and \(b\) is the \(y\)-intercept.

The slope of line (i) is \(m\).

Equation (ii) can be rewritten as:

\(-4y=-8x+12\)

\(y=\dfrac{-8x+12}{-4}\)

\(y=2x-3\)

The slope of this line is \(2\).

We know that the slopes of parallel lines are equal. So, \(m=2\).

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https://brainly.com/question/14874024

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