Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. 6x - 8y = 0 6x - 3y = 15 Add to eliminate x. Subtract to eliminate x. O Add to eliminate y. Subtract to eliminate y.

Answer 1

We have a system of linear equations:

`\begin{gathered} 6x-8y=0 \\ 6x-3y=15 \end{gathered}`

The simplest method to solve this is by substraction. In this case, we substract the second equation from the first one (NOTE: in this case, we don't need to multiply by any constant factor, but sometimes it is in order to have one of the variables eliminated).

Then, substracting both sides we would get:

`\begin{gathered} (6x-8y)-(6x-3y)=0-15 \\ 6x-6x-8y+3y=-15 \\ 0x-5y=-15 \\ -5y=-15 \\ y=3 \end{gathered}`

With the value of y, we can use any of the two equations to solve for x.

`\begin{gathered} 6x-8y=0 \\ 6x=8y \\ 6x=8\cdot3 \\ 6x=24 \\ x=(24)/(6) \\ x=4 \end{gathered}`

Answer: the first step is "Substract to eliminate x".