Question 669·Medium·Algebra

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The solution to the system of equations is $(x, y)$ .

\begin{cases} y = \tfrac12 x + 3 \\ x + 2y = 14 \end{cases}

What is the value of $y$ ?

Your answer

A system of linear equations gives two lines that must be true at the same point. Graph both equations in Desmos as written and click their intersection, the point where they cross. The second coordinate in $(x,y)$ is $y$ . The tempting slip is to submit the first coordinate when the question asks only for $y$ .

Hints

Hint 1
An intersection is a point shared by two graphs, so its coordinates make both equations true. Type each equation on its own Desmos line. Where do the lines cross?
Hint 2
An ordered pair lists coordinates as $(x,y)$ : $x$ comes first and $y$ comes second. After you click the crossing point, which number is in the second position?

Step-by-step

Read the intersection in Desmos
Step 1
Graph the first equation
Type $y=\frac12x+3$ on a Desmos line, without rearranging the equation. Its graph shows all the points that satisfy the first equation.
Step 2
Graph the second equation
Type $x+2y=14$ on a separate Desmos line, without rearranging either equation. Their intersection is the point that makes both equations true.
Step 3
Choose the coordinate the question asks for
Click their intersection. Desmos labels it $(4,5)$ . In $(x,y)=(4,5)$ , the second coordinate is $y=5$ . The first coordinate, $4$ , is $x$ , so don't enter it when the question asks for $y$ . Grid in 5.

Question 669·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this