Question

Elimination was used to solve a system of equations.

One of the intermediate steps led to the equation
3x = 18.
Which of the following systems could have led to
this equation?
4x + y = 20
x - y = 2
x + y = 4
x - 2y = 10
2x + y = 24
- x - y = 6
3x + y = 18
-3x - y = - 18

Answer 1

• x + y = 4
• x - 2y = 10

Explanation:

You want to know which set of equations could be combined in such a way as to result in the equation 3x = 18.

Set 1

• 4x +y = 20
• x -y = 2

To obtain a term of 3x, the second equation must be subtracted from the first. That will result in 3x +2y = 18, not the equation of interest.

Set 2

• x +y = 4
• x -2y = 10

A term of 3x can be obtained by adding twice the first equation to the second:

2(x +y) +(x -2y) = 2(4) +(10)

3x = 18 . . . . . as required

Set 3

• 2x +y = 24
• -x -y = 6

A term of 3x can be obtained by subtracting the second equation from the first. That will result in 3x +2y = 18, not the equation of interest.

Set 4

These equations are dependent. The second is the opposite of the first. They have an infinite number of solutions, not the single solution of the system of equations of interest.