Answer
\[x=-4,\ y=3\]
Work Step by Step
Multiply \[4\]on both sides to the equation \[x+2y=2\]to get: \[4x+8y=8\].
Add the second given equation to the above obtained equation from both RHS and LHS as follows:
\[\underline{\begin{align}
& 4x+8y=8 \\
& -4x+3y=25
\end{align}}\]
\[\begin{align}
& \ \ \ \ \ \ \ 11y=33 \\
& y=3
\end{align}\]
Put \[y=3\]in\[-4x+3y=25\], to get:
\[\begin{align}
& -4x+3\left( 3 \right)=25 \\
& -4x+9=25 \\
& -4x=16 \\
& x=-4
\end{align}\]
Put\[x=-4\]and \[y=3\]in any of the given equations to check the solution:
\[\begin{align}
& -4+2\left( 3 \right)=2 \\
& -4+6=2 \\
& 2=2
\end{align}\]
Since RHS\[=\]LHS, it implies the solution is correct.
Now check with -4x + 3y = 25 too:
-4(-4) + 3(3) = 25
16 + 9 = 25
25 = 25
LHS = RHS, so (-4,3) is a solution to the system of equations.
