Answer
The solution to this equation is $x = 10$ and $y = 13$. This system of equations is consistent because it has at least one solution. It is also independent because there is only one solution.
Work Step by Step
The equation gives $y$ in terms of $x$, so let's use this expression for $y$ to substitute into the second equation:
$6x - 4(x + 3) = 8$
Use distributive property first, paying attention to the signs:
$6x - 4x - 12 = 8$
Combine like terms:
$2x - 12 = 8$
Collect constant terms on the right side of the equation:
$2x = 20$
Divide each side of the equation by $2$ to solve for $x$:
$x = 10$
Now that we have the value for $x$, we can substitute it into the first equation to find $y$:
$y = 10 + 3$
Add to solve for $y$:
$y = 13$
Let's check the answer by substituting both values into one equation to see if both sides are equal:
$6(10) - 4(13) = 8$
Multiply first:
$60 - 52 = 8$
Subtract:
$8 = 8$
The solution to this equation is $x = 10$ and $y = 13$. This system of equations is consistent because it has at least one solution. It is also independent because there is only one solution.
