Answer
the solution of these linear equations will be \[x=6\], and \[y=-5\].
Work Step by Step
In the first equation, multiply with 3, and in the second equation multiply with \[-5\], and after that both the equations:
\[\begin{align}
& \left[ 5x+4y=10 \right]\times 3 \\
& \left[ 3x+5y=-7 \right]\times -5
\end{align}\]
After multiplication,
\[\begin{align}
& 15x+12y=30 \\
& -15x-25y=35
\end{align}\]
Add both equations,
\[\begin{align}
& \left( 15x-15x \right)+\left( 12y-25y \right)=\left( 30+35 \right) \\
& -13y=65 \\
& y=-5
\end{align}\]
Now, back substitute the value of y in any one of the equations.
\[\begin{align}
& 5x+4y=10 \\
& 5x+4\times -5=10 \\
& 5x-20=10 \\
& 5x=30
\end{align}\]
On solving,\[x=6\]
Therefore, the solution of these linear equations will be \[x=6\], and \[y=-5\].
