Question

Suppose you chose to solve the following system of equations by multiplying the first equation by 2 then by what number would you multiply the second equation to eliminate the variable by adding?

Answer 1

6

Step-by-step explanation:

Given the below system of equations;

`\begin{gathered} 4x-3y=6\ldots\ldots\ldots\text{Equation 1} \\ 6x+y=10\ldots\ldots\ldots\text{Equation 2} \end{gathered}`

If we multiply the first equation by 2, we'll have;

`8x-6y=12\ldots\ldots\text{.Equation 3}`

To be able to eliminate a variable by adding, we can notice that if multiply Equation 2 by 6. If we do, we'll have;

`36x+6y=60\ldots\ldots\ldots\text{Equation 4}`

If we add Equation 3 and 4, we'll have;

`\begin{gathered} (36+8)x+(-6+6)y=60+12 \\ 44x+0y=72 \\ 44x=72 \end{gathered}`

So if we multiply the second equation by 6, we will be able to eliminate a variable as seen above.