Question

Consider the system of linear equations below.

-3x + 4y +24
6x + 2 y+-18

Determine how to rewrite one of the two equations above in the form ax + by = c, where a, b, and c are constants, so that the sum of the new equation and the unchanged equation from the original system results in an equation of one variable.

Answer 1

6x + 2y - 18
-3x + 4y + 24

6x + 2y = 18
-3x + 4y = 24 (multiply both sides by 2)

6x + 2y = 18
-6x + 8y = 48
Add them together, and you get:

10y=66

Answer 2

-12x-4y=36

Explanation:

First, determine which variable will be eliminated. Next, consider how to create additive inverses with the coefficients on that variable by multiplying one of the two equations by a constant number.

To eliminate x by changing the first equation, the additive inverse of the coefficient of x in the second equation is needed. This is obtained by multiplying the first equation by 2 to get a coefficient of -6, the additive inverse of 6.

To eliminate x by changing the second equation, the additive inverse of the coefficient of x in the first equation is needed. This is obtained by multiplying the second equation by to get a coefficient of 3, the additive inverse of -3.

To eliminate y by changing the first equation, the additive inverse of the coefficient of y in the second equation is needed. This is obtained by multiplying the first equation by to get a coefficient of -2, the additive inverse of 2.

To eliminate y by changing the second equation, the additive inverse of the coefficient of y in the first equation is needed. This is obtained by multiplying the second equation by -2 to get a coefficient of -4, the additive inverse of 4.

Any of these four procedures can be used to begin the solving process. Once applied, the sum of the new equation and the unchanged equation from the original system is an equation of one variable.