ShmoopTube

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It's a bird! It's a plane! It's Shmooperman...guy!

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Find the positive x-coordinate of the point where the graphs of the equations…

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y = -2x squared - 6 y = -3x - 8 …intersect.

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Okay…so this question is asking us to solve for two linear equations.

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So, back in our old algebra days, we knew we had several methods that could help us do this…

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Solving by substitution…

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…solving by elimination…

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…or solving by graphing.

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So in this case we can do any of these, but the easiest would be to just set them equal,

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because…y equals y.

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So we have -2x squared – 6 equals -3x – 8.

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Now combine like terms and move everything to one side and we get:

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2x squared – 3x – 2 = 0

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…and that looks like a FACTORABLE quadratic equation.

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Easiest way to solve this equation is to factor by grouping.

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So if we split our -3x into x and -4x...

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...we get 2x squared + x - 4x - 2 = 0.

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This whole thing factors into x(2x + 1) - 2(2x + 1) = 0

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Now we both have x and -2 multiplied by the quantity 2x + 1.

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Do you know what we have to do next?

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Factor out that 2x + 1.

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Our final, fully factored equation is (2x + 1)(x-2) = 0.

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Well, when x = -1/2 and 2... this equation is true.

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Since the question asks for the positive x-coordinate, we'll take the positive 2.

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So the answer is…2. That’s where they intersect.

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