Would substitution or elimination be faster here? Look at the coefficients of $x$ and $y$ in the two equations and decide which method makes it easier to eliminate one variable.

Once you know $x$ and $y$, plug those values into the expression $2x - y$ and simplify carefully. Pay close attention to the minus sign.

In Desmos, type the two equations exactly as they are:

• 4x - y = 7
• x + 2y = 4 Desmos will display two lines on the coordinate plane.

Click on the point where the two lines intersect. Desmos will show the coordinates of this point; these are the values of $x$ and $y$ that solve the system.

Take the $x$ and $y$ coordinates from the intersection and type a new line in Desmos like 2*(x_value) - (y_value) using those numbers. The single number Desmos outputs is the value of $2x - y$ for the system’s solution.

We have the system

To find $x$ and $y$, we can use substitution or elimination. Here, elimination is convenient because we can quickly eliminate $y$ by combining the equations.

Multiply the second equation by $2$ so the coefficient of $x$ matches more closely with the first equation:

Now add this to the original first equation:

To solve more directly, another clean approach is to eliminate $y$ by making the coefficients opposites:

Multiply the first equation by $2$:

Now add this to the original second equation:

Substitute $x = 2$ back into one of the original equations, for example $x + 2y = 4$:

So the solution to the system is $(x, y) = (2, 1)$.

We are asked for the value of $2x - y$.

Substitute $x = 2$ and $y = 1$ into $2x - y$:

So, the value of $2x - y$ is 3.