Answer
\[x=-5,\ y=-2\]
Work Step by Step
The equation \[2x=3y-4\]can be written as \[2x-3y=-4\].
Multiply \[3\]on both sides to the equation \[2x-3y=-4\]to get: \[6x-9y=-12\].
Add the above obtained equation from both RHS and LHS as follows:
\[\underline{\begin{align}
& 6x-9y=-12 \\
& -6x+12y=6
\end{align}}\]
\[\begin{align}
& \ \ \ \ \ \ \ \ \ 3y=-6 \\
& y=-2
\end{align}\]
Put \[y=-2\]in\[2x-3y=-4\], to get:
\[\begin{align}
& 2x-3\left( -2 \right)=-4 \\
& 2x+6=-4 \\
& 2x=-10 \\
& x=-5
\end{align}\]
Put\[x=-5\]and \[y=-2\]in any of the given equations to check the solution:
\[\begin{align}
& -6\left( -5 \right)+12\left( -2 \right)=6 \\
& 30-24=6 \\
& 6=6
\end{align}\]
Since RHS\[=\]LHS, it implies the solution is correct.
For complete verification, we have to put x = -5 and y = -2 in 2x = 3y – 4 too.
2(-5) = 3(-2) – 4
-10 = -6 – 4
-10 = - 10
LHS = RHS
So, this is a solution to the above system of equations.
