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# Coordinates

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The lines -2x + y =k and 0.5x +y = 14 intersect when x= -8.4. What is the value of k?

Dec 9, 2021

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The two lines intersect when the y's and x's are equal. Thus, we can convert each to slope-intercept form:

$$y=2x+k, y=-0.5x+14$$

Thus, the lines intersect when $$2x+k = -0.5x+14 \text{ or } 2.5x=14-k$$.

Consequently, k = 14-2.5*-8.4 = 35.

Dec 9, 2021