Question 189·Medium·Algebra

Try adding the two equations together. This should give you an equation with only $m$, which you can then solve.

Once you know $m$, plug it into either original equation to get an equation in $n$ only, then solve that equation carefully.

After you solve the system, make sure you report the value of $n$, not $m$ or both coordinates.

Think of $m$ as $x$ and $n$ as $y$. Rewrite the equations solving for $n$:

• From $6m + 4n = 52$: $4n = 52 - 6m$, so $n = 13 - \frac{3}{2}m$.
• From $3m - 4n = 2$: $-4n = 2 - 3m$, so $n = \frac{3}{4}m - 0.5$.

In Desmos, you will use $x$ and $y$ instead of $m$ and $n$.

In the first expression line, type y = 13 - (3/2)x. This graphs the line that corresponds to $6m + 4n = 52$.

In the next expression line, type y = (3/4)x - 0.5. This graphs the line that corresponds to $3m - 4n = 2$.

Zoom or pan until you see where the two lines intersect. Tap the intersection point; Desmos will display its coordinates $(x, y)$. The $y$-coordinate of this point is the value of $n$ that solves the system.

Write the system:

The coefficients of $n$ are $+4$ and $-4$. If you add the two equations, the $n$ terms will cancel (be eliminated).

Add the left sides and the right sides:

This simplifies to:

Divide both sides by $9$ to get:

Use $m = 6$ in one of the original equations, for example $3m - 4n = 2$:

Simplify:

Now you have a single equation involving only $n$. Solve this for $n$.

From the equation

subtract $18$ from both sides:

Divide both sides by $-4$:

The question asks for the value of $n$, so the correct answer is $4$.