THIS USER ASKED 👇
Which value of m will create a system of parallel lines with no solution?
y=mx-6
8x-4y=12
THIS IS THE BEST ANSWER 👇
A system of parallel lines will be created where the two lines never meet and have no common solution of value m = 2
Step by step explanation:
The equation of the given line is 8 · x – 4 · y = 12
Giving;
8 · x- 12 = 4 · y
y = 2 · x – 3
Since the line passes through the points (0, -3) and (1, -1), we must;
When (x₁, y₁) = (0. -3) and (x₂, y₂) = (1, -1), we;
y – (-3) = 2 × (x – 0)
y = 2 · x – 3 which is the equation of the given line
For the lines 8 · x – 4 · y = 12, whose sane is y = 2 · x – 3 and whose line y = m · x – 6 has no solution, the slope of both lines should be equal to is m = 2
Since the line passes through the point (1.5, 0), we must;
y – 0 = 2 × (x – 1.5)
y = 2 · x – 3 ………………. (1)
For the equation, y = m · x – 6, when m = 2, we have;
y = 2 · x – 6 ……………… (2)
Gives equations of solutions (1) and (2);
2 · x – 3 = 2 · x – 6, which gives;
2 · x – 2 · x = – 3 – 6
0 = 9
Therefore, a system of parallel lines will be created where the two lines never meet and have no common solution of value m = 2.
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