Question 77·Medium·Systems of Two Linear Equations in Two Variables

The equation $2x + y = 4$ is easy to solve for $y$. Write $y$ in terms of $x$ and substitute into the other equation.

When you plug your expression for $y$ into $3x - 2y = 7$, remember that you are multiplying by $-2$, so distribute carefully.

After you find $x$ and $y$, make sure you compute $x - y$ (in that order), not $x + y$ or $y - x$.

Enter the two equations into Desmos:

• 3x - 2y = 7
• 2x + y = 4 Desmos will graph both lines.

Click on the point where the two lines intersect. Desmos will display its coordinates $(x_0, y_0)$; these are the solution values for $x$ and $y$.

In a new expression line, type x0 - y0 but replace x0 and y0 with the actual $x$- and $y$-coordinates you read from the intersection point. The value shown is the $x - y$ that you should match to one of the answer choices.

Look at the second equation:

Solve it for $y$:

Now you have $y$ written in terms of $x$.

Substitute $y = 4 - 2x$ into the first equation $3x - 2y = 7$:

Distribute $-2$:

Combine like terms:

Add 8 to both sides:

Divide by 7:

Use $y = 4 - 2x$ and substitute $x = \frac{15}{7}$:

Compute $2 \cdot \frac{15}{7} = \frac{30}{7}$ and write $4$ as $\frac{28}{7}$:

So the solution to the system is $\left(\frac{15}{7}, -\frac{2}{7}\right)$.

Now use the values of $x$ and $y$ to find $x - y$:

So $x - y = \frac{17}{7}$, which corresponds to answer choice C.