Find the value of $a^2-b^2+c^2$ Let $a$, $b$, and $c$ be real numbers such that $a − 7b + 8c = 4$ and $8a + 4b − c = 7$. What is the
value of $a^2-b^2+c^2$ ?

You can also do it solving the two equations for $b$ and $c$ to be expressed as functions of $a$. This would give $$b=\frac{12}{5}-\frac{13 a}{5}\qquad c=\frac{13}{5}-\frac{12 a}{5}$$ Now, replace in the expression, expand and simplify.
