Question

As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor should she multiply both sides of the other equation so that she can add the equations and eliminate a variable?

Answer 1

Suppose that Yumiko has the linear system

`2x-3y=12 \;;(1)\\ax+by=c \;; (2)`

Since she multiplies the first equation by 6 then she obtains the equation

`12x-18y=72`

Then, if she want to eliminate the variable y, she should multiply the equation (2) by
`(-12)/(a)` because when performing the multiplication, the coefficient that accompanies the x become 12.

If she want to eliminate the variable y, she should multiply the equation (2) by
`(3)/(b)` because when performing the multiplication, the coefficient that accompanies the y become 3.