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3 years ago

For what value of k are the lines 2x + 3y = 4k and x - 2ky = 7 parallel?

Mathematics

1 answer:

natulia [17]3 years ago

5 0

Answer:

k = -3/4

Step-by-step explanation:

The lines will be parallel if their slopes are equal. To find the slope of each line, write its equation in slope-intercept form (y = mx + b). In other words, solve each equation for y and look at the coefficient of x.

2x + 3y = 4k

3y = -2x + 4k

y = (-2/3)x + 4k/3

The slope of the first line is -2/3.

x - 2ky = 7

-2ky = -x + 7

y = [1/(2k)]x - 7/(2k)

The slope of the second line is 1/(2k).

If the slopes are equal, then

1/(2k) = -2/3

Multiply by 2k.

1 = (-2/3)(2k) = (-4/3)k

1 = (-4/3)k

k = -3/4

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