Question

Two systems of equations are shown below:. System A. 3x + 2y = 3. –2x - 8y = –1. System B. –x - 14y = 1. –2x – 8y = –1. Which of the following statements is correct about the two systems of equations?. The value of x for System B will be one–third of the value of x for System A because the coefficient of x in the first equation of System B is one third times the coefficient of x in the first equation of System A.

Answer 1

We can solve for both x and y of System A and B to compare the values of x.

System A. Multiply by 4 the first equation and add both equations,
                                         12x + 8y = 12
                                   +     -2x - 8y = -1
We will be left with equation, 
                                         10x = 11
The value of x is 11/10

System B. Multiply the first equation by -2 and add the equations,
                                     2x + 28y = -2
                             +     -2x - 8y = -1
We will be left with 20y = -3. Substitute the value of y to any of the equations. This gives a value of x equal to 11/10. 

The answer therefore is that both systems will have the same value of x's.
                                 

Answer 2

To compare the values of x, we need to obtain the values of x for both systems.

For system A. Multiply the first equation by 4 and add the equations,
                                         12x + 8y = 12
                                   +     -2x - 8y = -1
It will yield, 
                                         10x = 11
Then, the value of x is 11/10.

For system B. Multiply the first equation by -2 and add the equations given,
                                     2x + 28y = -2
                             +     -2x - 8y = -1
It will yield,
20y = -3
 
We substitute the value of y to any of the equations in system B. This gives a value of x which is equal to 11/10. 

Therefore, both systems will have the same value of x.