Test 8 Section 3 #14

The fastest way to figure out how many solutions a system of equations will have if you can’t just graph them (this is the no calculator section) is to set both equations equal to y, then substitute and solve.

    \begin{align*}y&=x^2+3x-7\\\\y-5x+8&=0\\y&=5x-8\\\\5x-8&=x^2+3x-7\\0&=x^2-2x+1\\0&=(x-1)^2\end{align*}

Because the only value that makes that equation true is x = 1, the system of equations only has one solution.

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