Question

Elimination was used to solve a system of equations.

One of the intermediate steps led to the equation 2x = 8.
Which of the following systems could have led to this equation?
3x - y = 15
x + y = 7
x + 3y = 24
- x - 3y = 16
4x + 2y = 14
x + y = 3
2x+2y = 8
- 2x - 2y=8

Answer 1

(c) 4x + 2y = 14; x + y = 3

Explanation:

The given equation will be the result of eliminating the y-variable from the system. When we do that for the different answer choices, we get ...

a

Add the two equations: (3x -y) +(x +y) = (15) +(7) ⇒ 4x = 22

b

Add the two equations: (x +3y) +(-x -3y) = (24) +(16) ⇒ 0 = 40

c

Subtract twice the second from the first.

(4x +2y) -2(x +y) = (14) -2(3) ⇒ 2x = 8 . . . . the system we're looking for

d

Add the two equations: (2x +2y) +(-2x -2y) = (8) +(8) ⇒ 0 = 16

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Additional comment

When the equation reduces to 0 = constant, and "constant" is not zero, it means the system of equations has no solution. (The equations describe parallel lines.)