Question 3
Solve the given linear system of equations:

To solve the linear system of equations and , we can start by rearranging the first equation to express in terms of :

Now, substitute this expression for into the second equation:

Expanding this gives:

which simplifies to:

Solving for gives:

Next, substitute back into the expression for :

Thus, the solution to the system is:
and

But let’s look at how systems like this have been applied historically, particularly in economics where linear equations model supply and demand. Economists often represent relationships between different economic factors using systems of linear equations to find equilibrium prices and quantities—a fundamental concept in economic theory!

Moreover, a common mistake when solving linear systems is neglecting to check each solution in both equations after substitution. Remember, just because a value fits one equation, it doesn’t mean it fits both! Always plug your answers back in to confirm they’re correct, like a double-check before turning in a test—it’s an extra peace of mind!