### Home > CCA2 > Chapter 10 > Lesson 10.2.1 > Problem 10-101

10-101.

Solve for

*x*and*y*in each system below.*10-101 HW eTool*(Desmos). Homework Help ✎2

*x*+*y*= 12

*xy*= 162

*x*+*y*= 12

*xy*= 20Explain how the graphs of (a) and (b) relate to the solutions to each system of equations.

Note that other sequences of steps are possible.

When *x* = 4, *y* = 4, so (4, 4) is a solution.

When *x* = 2, *y* = 8, so (2, 8) is a solution.

Now try part (b) on your own.

*y* = 12 − 2*x*

*x*(12 − 2*x*) = 16

12*x* − 2*x*^{2} − 16 = 0

*x*^{2} − 6*x* + 8 = 0

(*x* − 4)(*x* − 2) = 0

*x* = 4 or *x* = 2

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