Instead of solving for $x$ and $y$ separately, ask: can you combine the two equations to directly create the expression $7x + 3y$?

After clearing fractions, you have $5x+4y=\text{?}$ and $2x-y=\text{?}$. What happens to the $x$ and $y$ coefficients if you add these equations together? How does that relate to $7x+3y$?

Type the cleared-fraction versions directly:

• 5x + 4y = 21
• 2x - y = 3

Desmos will graph both lines.

Click or tap on the point where the two lines intersect. Desmos will label it as something like $(x_1, y_1)$.

In a new expression line, type 7x1 + 3y1. Desmos will show a numerical result; this is the value of $7x + 3y$ for the solution of the system.

Multiply both equations by 3 to remove the denominators:

• First equation: $\dfrac{5}{3}x + \dfrac{4}{3}y = 7$
  • Multiply by 3: $5x + 4y = 21$
• Second equation: $\dfrac{2}{3}x - \dfrac{1}{3}y = 1$
  • Multiply by 3: $2x - y = 3$

Now the system is:

We want the value of $7x + 3y$ at the solution of the system.

Look at the left sides:

• First equation: $5x + 4y$
• Second equation: $2x - y$

If you add the two equations side by side:

• Left side: $(5x + 4y) + (2x - y) = 7x + 3y$
• Right side: $21 + 3$

So adding the equations gives a new equation of the form

We now just need to evaluate the right-hand side.

From the combined equation

we compute $21 + 3 = 24$.

So $7x + 3y = 24$, which corresponds to answer choice C) 24.