Solving two equations, one with a square root

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Question from kacie, a student:

y = square root of x+3
x-4y = -7

im having trouble with this problem...i have to find where they intersect.

Hi Kacie,

I would square both sides of the first equation to get

y² = x + 3

and the write this expression as

x = y² - 3.

Substitute this value for x into the second equation and solve for y.

You need to be careful using this technique as the squaring in the first step might result in extraneous solutions so you need to verify any solutions you found by solving the quadratic.

I hope this helps,
Harley

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