Solve the following linear systems of equations.
For additional practice, make up your own systems of equations. Use \wolfA or the SageCell below to check your work.
\(\begin{cases}x+y\amp =3\\2x-y\amp =4 \end{cases}\)
\(\begin{cases}-x + 4y\amp =8\\3x - 12y\amp =2 \end{cases}\)
Find all solutions to the linear system \(\begin{cases}x+y+z\amp =3\\2x-y\amp =4 \end{cases}\text{.}\) Since there are more variables than equations, this suggests there is probably not just one solution, but perhaps infinitely many. One common way to deal with solving such a system is to let one variable equal \(t\text{,}\) and then solve for the other variables in terms of \(t\text{.}\) Do this three different ways.
This link will show you how to specify which variable is \(t\) when using Wolfram Alpha.
If you let \(x=t\text{,}\) what are \(y\) and \(z\text{.}\) Write your solution in the form \((x,y,z)\) where you replace \(x\text{,}\) \(y\text{,}\) and \(z\) with what they are in terms of \(t\text{.}\)
If you let \(y=t\text{,}\) what are \(x\) and \(z\) (in terms of \(t\)).
If you let \(z=t\text{,}\) what are \(x\) and \(y\text{.}\)