Question 304·Easy·Algebra

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The system of equations is

\begin{cases} 3x - y = 5 \\ x = 4 \end{cases}

The solution to the system is $(x, y)$ . What is the value of $y$ ?

A system of equations asks for values that make both equations true. If one equation fixes $x$ , graph both equations as written in Desmos and click their intersection. In an ordered pair $(x,y)$ , the second coordinate is $y$ . The trap is reading the first coordinate when the question asks for the second.

Hints

Hint 1
A system uses the same pair $(x,y)$ in both equations. One equation already fixes the first coordinate. What kind of line contains every point with that $x$ -value?
Hint 2
The intersection is where the two lines meet, so its coordinates satisfy both equations. After you click it, read the second coordinate to find $y$ .

Step-by-step

Graph the system in Desmos
Step 1
Identify the fixed coordinate
A system uses the same pair $(x,y)$ in both equations. Since $x=4$ , the solution must lie on the vertical line $x=4$ ; its $y$ -value is still unknown.
Step 2
Click the intersection and read y
Type $3x-y=5$ and $x=4$ on separate Desmos lines. Click their intersection, where both equations hold. Desmos shows $(4,7)$ . The second coordinate is $y$ , so $y=7$ . Choice C.

Question 304·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this