To solve the system of equations using elimination, we have the following two equations:
- \(-3x - 4y = -23\)
- \(3x - 5y = 5\)
Let's manipulate these equations to eliminate one of the variables. Here, we can add the two equations together since the coefficients of \(x\) in the first equation is \(-3\) and in the second equation is \(3\), which will eliminate \(x\):
- \(-3x - 4y = -23\)
- \(+3x - 5y = 5\)
Adding the two equations:
\[ (-3x + 3x) + (-4y - 5y) = -23 + 5 \] \[ 0x - 9y = -18 \]
This simplifies to:
\[ -9y = -18 \]
To solve for \(y\), divide both sides by \(-9\):
\[ y = 2 \]
Now that we have the value of \(y\), we can substitute it back into one of the original equations to find \(x\). Let's use the second equation:
\[ 3x - 5y = 5 \] Substituting \(y = 2\):
\[ 3x - 5(2) = 5 \] \[ 3x - 10 = 5 \] Now we add \(10\) to both sides:
\[ 3x = 15 \] And divide by \(3\):
\[ x = 5 \]
Thus, the solution to the system of equations is:
\((5, 2)\)
Therefore, the response is:
(5, 2)