Answer
The solution to this equation is $n = -3$ and $H = \frac{31}{5}$.
Work Step by Step
The equation gives $H$ in terms of $n$, so let's use this expression for $H$ to substitute into the second equation:
$2n + 10(\frac{3}{5}n + 8) = 56$
Use distributive property first, paying attention to the signs:
$2n + 6n + 80 = 56$
Combine like terms:
$8n + 80 = 56$
Collect constant terms on the right side of the equation:
$8n = -24$
Divide each side of the equation by $8$ to solve for $n$:
$n = -3$
Now that we have the value for $n$, we can substitute it into the first equation to find $H$:
$H = \frac{3}{5}(-3) + 8$
Multiply first:
$H = \frac{-9}{5} + 8$
Convert $8$ to a fraction that has $5$ as its denominator so we can add the two fractions:
$H = \frac{-9}{5} + \frac{40}{5}$
Add the fractions:
$H = \frac{31}{5}$
The solution to this equation is $n = -3$ and $H = \frac{31}{5}$.
Let's check the answer by substituting both values into one of the original equations to see if both sides are equal:
$2(-3) + 10(\frac{31}{5}) = 56$
Multiply first:
$-6 + 62 = 56$
Add:
$56 = 56$
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.
