Question

Given that the value of b can never be equal to -1, determine if the equations are intersecting, parallel, or coincident.

Answer 1

Answer: A) intersecting

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Work Shown:

Solve the first equation for y

x+y = ab

y = -x+ab

y = -1x + ab

slope = -1, y intercept = ab

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Solve for y in the second equation

bx - y = a

bx - y - a = 0

bx-a = y

y = bx - a

Slope = b, y intercept = -a

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The first equation has a slope of -1. The second equation has a slope of b.

Since b cannot equal -1, this means the two equations have different slopes. It is impossible for these two lines to be parallel, because parallel lines have equal slopes. The different slope values tell us the lines cross at exactly one point.