$$4x-y=a$$ $$3x+2y=7$$

In the system of equations above, $a$ is a constant. What is the $x$-value of the solution to the system in terms of $a$?

Summary Submit

We can use either substitution or elimination, but we need to make sure to eliminate or substitute the value of $y$ since we want $x$ in terms of $a$. Below I show substitution.

$$4x-y=a$$ $$y=4x-a$$

Substituting the value of $y$.

$$3x+2y=7$$ $$3x+2(4x-a)=7$$

Solving for $x$ in terms of $a$.

$$3x+8x-2a=7$$ $$11x=7+2a$$ $$x=\boxed{\frac{2a+7}{11}}$$