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Math Question for Friday, January 30th, 2015

If *x* + 2*y* = 1, and 2*x* + *y* = 5, then *x* + *y* = ?

**F.** 1

**G.** 2

**H.** 3

**J.** 4

**K.** 5

## Incorrect

## Correct!

**The correct answer is G.**

If *x* + 2*y* = 1, then *x* = 1 – 2*y*.
Substituting into 2*x* + *y* = 5, 2(1 – 2*y*) + *y* = 5, 2 – 4*y* + *y* = 5, 2 – 3*y* = 5,
–3*y* = 3, *y* = –1. Then *x* = 1 – 2(–1) = 1 + 2 = 3.

Check: If *x* = 3 and *y* = –1, 3 + 2(–1) = 3 – 2 = 1 and 2(3) + (–1) = 6 – 1 = 5,

so the solution for the system is *x* = 3 and *y* = –1 and then *x* + *y* = 2.

**F, H, J, K.** *x* + 2*y* = 1 and 2*x* + *y* = 5 are different nonparallel lines because the slope of the first line is – and the slope of the second line is –2. Different nonparallel lines intersect in at most one point and that point is (3,–1). The sum of any two numbers is unique, so none of the other answers can be correct.

## Incorrect

## Incorrect

## Incorrect