Question 173·Medium·Math

Try letting a new variable, such as $x$, stand for $2y+7$. Rewrite the entire equation using $x$ instead of $2y+7$.

After you solve the equation in terms of your new variable (like $x$), remember that this variable represents $2y+7$. Use that value directly to select the correct answer choice.

In Desmos, let $x$ stand for $2y+7$ by simply working with $x$ in place of $2y+7$. You do not need to define $y$ explicitly; just solve in terms of $x$.

Enter y = 5x - 3 and y = 2x + 12 as two separate expressions. These represent the two sides of the equation after substitution.

Tap on the point where the two lines intersect. The x-coordinate of this intersection is the solution for $x$, which is also the value of $2y+7$. Match that x-value to the correct answer choice.

The expression $2y+7$ appears on both sides of the equation:

This suggests we can treat $2y+7$ as a single unit to make the equation simpler.

Let $x = 2y + 7$.

Then the equation becomes

Now you just need to solve this linear equation for $x$.

Solve $5x - 3 = 2x + 12$ step by step:

• Subtract $2x$ from both sides:

• Add 3 to both sides:

• Divide both sides by 3:

Do not simplify this final fraction to a number just yet in this step.

From the last step, $x = \frac{15}{3}$, so $x = 5$.

But $x$ was defined as $2y + 7$, so

Therefore, the value of $2y + 7$ is $\boxed{5}$, which corresponds to answer choice C.