Question

You decide to multiply the top equation to eliminate x's. What do you need to multiply the top equation by so you can add the equations to eliminate x?

a) 3
b) 2
c) -3
d) -2

Answer 1

To eliminate x in a system of equations, the top equation is multiplied by a factor that makes its x coefficient the negative reciprocal of the x coefficient in the other equation. For an x coefficient of 1, the factor is -3; for 2/3, it is -2.

Step-by-step explanation:

To eliminate x from a system of equations by addition, one must multiply one or both of the equations by a certain factor so that when the equations are added together, the x terms cancel each other out. Without specific equations provided, we consider a general case where one equation has x and the other has a multiple of x, say 3x. To cancel 3x by adding, the first equation's x would need to become -3x through multiplication. Therefore, multiplying the top equation with either a -3 or a -2 does this, depending on whether the coefficient in front of x in the top equation is 1 or 2/3 respectively.

If the top equation's coefficient of x is 1, we multiply by -3. If it is 2/3, we would multiply by -2 to obtain a coefficient that is the negative reciprocal of 3x. This concept is critical when you are solving systems of linear equations by elimination.