Question

Here is a system of linear equations: Which would be more helpful for solving the system: adding the two equations or subtracting one from the other? Explain your reasoning. Solve the system without graphing. Show your work.

Answer 1

Okay, here we have this:

Considering the provided system we obtain the following:

The option more helpful for solving the system is add one equation to the other because in this way we can cancel the term of the "y", if we solve the system we obtain the following:

`\begin{bmatrix}2x+(1)/(2)y=7 \\ 6x-(1)/(2)y=5\end{bmatrix}`

Adding the equations:

`\begin{gathered} 8x=12 \\ x=(12)/(8) \\ x=(3)/(2) \end{gathered}`

Now, let's replacing in the first equation with x=3/2:

`\begin{gathered} 2((3)/(2))+(1)/(2)y=7 \\ 3+(1)/(2)y=7 \\ (y)/(2)=4 \\ y=8 \end{gathered}`

Finally we obtain that the solution to the system is x=3/2 and y=8.