Question 184·Easy·Algebra

Take the expression for $y$ from the first equation and plug it into the second equation wherever you see $y$.

After substituting, combine like terms to solve for $x$. Then plug that $x$-value back into $y = 2x + 1$ to get $y$.

Whatever $x$ and $y$ you find must make both equations true. If a value only works in one equation, it cannot be correct.

In Desmos, enter the equation y = 2x + 1. This will draw the first line.

Enter the second equation. You can either type x + y = 7 directly (Desmos will graph it) or rewrite it as y = 7 - x and enter that. This will draw the second line.

On the graph, tap or click where the two lines intersect. Desmos will display the coordinates $(x, y)$ of this point. The $y$-value shown there is the answer to the question.

You are given the system

The first equation already expresses $y$ in terms of $x$. This makes it convenient to substitute into the second equation.

Replace $y$ in the second equation with the expression $2x+1$ from the first equation.

Starting with $x + y = 7$:

Now all terms are in terms of $x$, so you can solve for $x$.

Combine like terms and solve the equation:

Now that you know $x$, you can find $y$ using $y = 2x + 1$.

Substitute $x = 2$ into $y = 2x + 1$:

So the value of $y$ is $5$, which corresponds to answer choice C.