Question

Elimination was used to solve a system of equations.
One of the intermediate steps led to the equation 9x = 27.
Which of the following systems could have led to this equation?
O
9x + 2y = 21
-9x – 2y = 21
10x – y = 15
x+y = – 12
7x – 2y = 15
x + y = 6
4x + 3y = 24
-5x – 3y = 3

1. hongcuc2
The system of equation that could have led to the equation 9x = 27 is
7x – 2y = 15
x + y = 6
The correct option is the third option
7x – 2y = 15
x + y = 6

### Solving systems of equations

From the question, we are to determine the system that could have led to 9x = 27
1.
9x + 2y = 21
-9x – 2y = 21
Subtracting, we get
9x + 2y = 21
-9x – 2y = 21
——————-
18x + 4y = 0
2.
10x – y = 15
x + y = – 12
Subtracting, we get
10x – y = 15
x + y = – 12
———————
9x -2y = 27
3.
7x – 2y = 15
x + y = 6
Here, multiply the second equation by 2
2 × [x + y = 6]
2x + 2y = 12
Now, add to the first equation
7x – 2y = 15
2x + 2y = 12
——————
9x = 27
4.
4x + 3y = 24
-5x – 3y = 3
Subtracting, we get
4x + 3y = 24
-5x – 3y = 3
———————
9x + 6y = 21
Hence, the system of equation that could have led to the equation 9x = 27 is
7x – 2y = 15
x + y = 6
The correct option is the third option
7x – 2y = 15
x + y = 6