Answer
The solution to this system of equations is $(-\frac{5}{2}, \frac{5}{2})$.
Work Step by Step
We can solve this system of equations by the substitution method. We pick the simpler equation, the first one:
$x + 3y = 5$
We solve the equation for $x$ by subtracting $3y$ from each side of the equation:
$x = -3y + 5$
We use this value for $x$ to substitute into the second equation to find the value for $y$:
$-2(-3y + 5) - 4y = -5$
Use distributive property to get rid of the parentheses:
$6y - 10 - 4y = -5$
Add $10$ to both sides to isolate constants to the right side of the equation:
$6y - 4y = 5$
Subtractg the $y$ terms:
$2y = 5$
Divide both sides by $2$ to solve for $y$:
$y = \frac{5}{2}$
Now, we use this value of $y$ and substitute it back into the first equation to solve for $x$:
$x + 3(\frac{5}{2}) = 5$
Do the multiplication:
$x + \frac{15}{2} = 5$
Subtract $\frac{15}{2}$ from both sides of the equation to solve for $x$:
$x = \frac{10}{2} - \frac{15}{2}$
Subtract the fractions:
$x = -\frac{5}{2}$
The solution to this system of equations is $(-\frac{5}{2}, \frac{5}{2})$.
