Question

How many solutions are there to the equation blow? 17x-8=3x+16

Answer 1

The given equation is equivalent to the system

`\begin{cases}y = 17x-8\\y = 3x+16\end{cases}`

The linear equations have different slopes (m = 17 and m = 3), so that means the two lines intersect at exactly one location. This one intersection point means there is exactly one solution to the system.

That means there is exactly one solution to the equation 17x-8 = 3x+16

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That solution is....

17x-8 = 3x+16

17x-3x = 16+8

14x = 24

x = 24/14

x = 12/7