Answer
The solution to this equation is $x = -4$ and $y = \frac{7}{2}$.
Work Step by Step
The second equation gives $x$ in terms of $y$, so let's use this expression for $x$ to substitute into the first equation:
$5(2y - 11) - 8y = -48$
Use distributive property first, paying attention to the signs:
$10y - 55 - 8y = -48$
Combine like terms:
$2y - 55 = -48$
Collect constant terms on the right side of the equation:
$2y = 7$
Divide each side of the equation by $2$:
$y = \frac{7}{2}$
Now that we have the value for $y$, we can substitute it into the first equation to find $x$:
$x = 2(\frac{7}{2}) - 11$
Multiply first:
$x = 7 - 11$
Subtract to solve:
$x = -4$
The solution to this equation is $x = -4$ and $y = \frac{7}{2}$.
Let's check the answer by substituting both values into one of the original equations to see if both sides are equal:
$5(-4) - 8(\frac{7}{2}) = -48$
Multiply first:
$-20 - 28 = -48$
Add:
$-48 = -48$
The two sides are equal; therefore, this solution is correct.
This system of equations is consistent because it has at least one solution. It is also independent because there is only one solution.
