Find all pairs of real numbers (x,y) such that x + y = 6 and x^2 + y^2 = 28. If you find more than one pair, then list your pairs in order by increasing x value, separated by commas. For example, to enter the solutions (2,4) and (-3,9), you would enter "(-3,9),(2,4)" (without the quotation marks).

Question

Find all pairs of real numbers (x,y) such that x + y = 6 and x^2 + y^2 = 28. If you find more than one pair, then list your pairs in order by increasing x value, separated by commas. For example, to enter the solutions (2,4) and (-3,9), you would enter "(-3,9),(2,4)" (without the quotation marks).

Answer 1

You can always tell a lazy clod -- they copy the instructions for submitting the answer.

To do this, just substitute one equation into the other:

x+y=6 means y = 6-x

So,

x^2+y^2 = 28
x^2 + (6-x)^2 = 28
x^2 + x^2-12x+36 = 28
2x^2 - 12x + 8 = 0
2(x^2-6x+4) = 0

Now it's easy, right?