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

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 \(a\).

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