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?5x + 6y = 182x – 3y = 12factor:

Answer 1

Given the equations

$\begin{cases}5x+6y=18 \\ 2x-3y=12\end{cases}$

First, she multiplied the second equation by 6:

$\begin{gathered} 6\cdot(2x-3y)=6\cdot12 \\ 6\cdot2x-6\cdot3y=6\cdot12 \\ 12x-18y=72 \end{gathered}$

You have to determine the factor to multiply the equation 5x+6y=18 to be able to add both equations and eliminate one of the variables.

To do so, compare the coefficients of the like terms:

5x and 12x, "12" is not a multiple of 5, so there is no factor that when multiplied by 5x will give 12x as a product.

6y and 18y, 18 is a multiple of 6, if you multiply 6y by 3 the product will be 18y.

So, the factor you have to use to multiply the equation and eliminate one variable is 3.