Question 41·Medium·Systems of Two Linear Equations in Two Variables

Look at the coefficients of $y$ in the two equations: $-2$ and $5$. What can you multiply each equation by so that the $y$-terms become opposites (like $+10y$ and $-10y$)?

After you multiply to make the $y$-coefficients opposites, add the resulting equations together. What expression involving $x$ appears on the left side? What numerical expression appears on the right?

Once you have an equation whose left side is $43x$, simplify the right side with basic subtraction. That final simplified number is the value of $43x$.

Rewrite each equation in the form $y = mx + b$ and enter them:

• From $7x - 2y = 11$, solve for $y$ to get $y = \frac{7x - 11}{2}$, then type y = (7x - 11)/2.
• From $4x + 5y = -13$, solve for $y$ to get $y = \frac{-13 - 4x}{5}$, then type y = (-13 - 4x)/5.

You will see two lines on the graph.

Click on the point where the two lines intersect. Desmos will display the coordinates of this point as $(x, y)$. Note the $x$-value from this intersection.

In a new expression line, type 43 * followed by the $x$-value you read from the intersection point (for example, 43 * (0.67) or using the exact fraction if shown). The resulting output is the value of $43x$, which matches one of the answer choices.

The system is

Since the question asks for $43x$, try to eliminate $y$ so you get an equation involving only $x$. This is efficient because once you have a single equation in $x$, you can quickly find $43x$ without solving for $y$ at all.

To eliminate $y$, make the coefficients of $y$ in the two equations opposites.

• The first equation has $-2y$.
• The second equation has $+5y$.

A common multiple of $2$ and $5$ is $10$. Multiply:

• The first equation by $5$:

• The second equation by $2$:

Now the $y$-terms are $-10y$ and $+10y$, which will cancel when added.

Add the two new equations term by term:

• Left side: $35x + 8x$ becomes $43x$, and $-10y + 10y$ becomes $0$.
• Right side: $55 + (-26)$ becomes $55 - 26$.

So after adding, you get a single equation in $x$:

Compute the right-hand side:

So the equation becomes

The question asks for the value of $43x$, which is $29$. That corresponds to answer choice D.