Solve the following system using augmented matrix methods:

(a) The initial matrix is:

 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\end{array}}\right|$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

(b) First, perform the Row Operation $\frac{1}{4} R_1 \to R_1$. The resulting matrix is:

 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\end{array}}\right|$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

(c) Next, perform the operation $-5 R_1 + R_2 \to R_2$. The resulting matrix is:

 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\end{array}}\right|$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

(d) Finish simplifying the augmented matrix. The reduced matrix is:

 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\end{array}}\right|$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

(e) How many solutions does the system have? If infinitely many, enter "Infinity".

(f) What are the solutions to the system?

If there are no solutions, write "No Solution" or "None" for each answer. If there are infinitely many solutions let $y = t$ and solve for $x$ in terms of $t$.

$x=$
$y=$

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