Question

What is the value of x in the solution to the following system of equations?

Answer 1

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$\begin{cases}&x-y=-3\quad\Longrightarrow\ Eq.\ 1\\&x+3y=5\quad\Longrightarrow\ Eq.\ 2\end{cases}\\ \\ \\x=-3+y\\ \\\textbf{Add\ "x"\ in\ Eq.\ 2}\\ \\-3+y+3y=5\\ \\4y-3=5\\ \\4y=5+3\\ \\4y=8\\ \\y= \dfrac{8}{4}\\ \\y=2\quad\checkmark\\ \\\textbf{Add\ "y"\ in\ Eq.\ 1}\\ \\x-2=-3\\ \\x=-3+2\\ \\x=-1\quad\checkmark\\ \\ \\\mathbb{ANSWER:}\\ \\\boxed{\boxed{\quad\boldsymbol{x=-1\ ;\ y=2}\quad}}\\ \\ \\\textbf{HOPE\ THIS\ HELPS...!!}$

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Answer 2

We can easily eliminate x.  To do this, mult. the 1st eqn by -1:  -x + y = 3

and add this result to the second equation:

-x + y = 3
x + 3y = 5
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       4y = 8   Then y = 2.  Sub 2 for y in the 2nd equation:  x + 3(-2) = 5
                                                                                             x            = 5+6
                    Then x = 11

The solution is (11, 2).