Answer
\[x=4,\ y=5\]
Work Step by Step
The equation \[2x-y=3\]can be written as follows:
\[\begin{align}
& 2x-y=3 \\
& -y=3-2x \\
& y=2x-3
\end{align}\]
Substitute\[y=2x-3\]in the equation\[5x-2y=10\], to get:
\[\begin{align}
& 5x-2\left( 2x-3 \right)=10 \\
& 5x-4x+6=10 \\
& x+6-6=10-6 \\
& x=4
\end{align}\]
Substitute \[x=4\]in\[y=2x-3\], to get:
\[\begin{align}
& y=2\left( 4 \right)-3 \\
& =8-3 \\
& =5
\end{align}\]
Put\[x=4\]and \[y=5\]in any of the given equations to check the solution:
\[\begin{align}
& 5\left( 4 \right)-2\left( 5 \right)=10 \\
& 20-10=10 \\
& 10=10
\end{align}\]
Since RHS\[=\]LHS, it implies the solution is correct.
Now, put x = 4 and y = 5 in 2x – y = 3.
2(4)-5 = 3
3 = 3
So, (4,5) is a solution to this system of equations.
