Answer
The solution to this system of equations is $(0, -5)$.
Work Step by Step
We need to use the substitution method to solve this system of equations. Therefore, we need to express one variable in terms of another. Let's choose to solve the first equation for $y$ in terms of $x$:
$7y = 14x - 35$
Divide both sides by $7$ to isolate the $y$ variable:
$y = 2x - 5$
We can now substitute $y=2x-5$ in the second equation:
$-25-6x=5y\\
-25 - 6x = 5(2x - 5)$
$-25 - 6x = 10x - 25$
Add $25$ to each side to shift constants to the right side of the equation:
$- 6x = 10x - 25 + 25$
Subtract $10x$ from each side of the equation to move the variable to the left side of the equation:
$- 6x - 10x = - 25 + 25$
$-16x = 0$
Divide each side by $-16$ to solve for $x$:
$x = 0$
Now that we have the value for $x$, we can substitute this value into the first equation to solve for $y$:
$14(0) - 35 = 7y$
$-35=7y$
Divide each side by $7$ to solve for $x$
$-5=y$
The solution to this system of equations is $(0, -5)$.
