Answer
\[x=-2,\ y=-4\]
Work Step by Step
Multiply \[10\]on both sides to the equation,\[2x+3y=-16\]to get: \[20x+30y=-160\].
Multiply \[3\]on both sides to the equation,\[5x-10y=30\]to get: \[15x-30y=90\].
Add the above obtained equation from both RHS and LHS as follows:
\[\underline{\begin{align}
& 20x+30y=-160 \\
& 15x-30y=90
\end{align}}\]
\[\begin{align}
& 35x\ \ \ \ \ \ \ \ \ \ =-70 \\
& x=-2
\end{align}\]
Put \[x=-2\]in\[2x+3y=-16\], to get:
\[\begin{align}
& 2\left( -2 \right)+3y=-16 \\
& -4+3y=-16 \\
& 3y=-12 \\
& y=-4
\end{align}\]
Put\[x=-2\]and \[y=-4\]in any of the given equations to check the solution:
\[\begin{align}
& 5\left( -2 \right)-10\left( -4 \right)=30 \\
& -10+40=30 \\
& 30=30
\end{align}\]
Since RHS\[=\]LHS, it implies the solution is correct.
Now check its solution with 2x + 3y = -16 too.
2(-2) +3(-4) = -16
-4 – 12 = - 16
- 16 = -16
So, LHS = RHS.
Now, we can say that x = -2 and y = -4 is a solution to this system of equations.
