Question 534·Medium·Algebra

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The system of equations is

$y = 2x + 1$

$4x - y = 5$

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

A system of equations gives two conditions that the same pair $(x,y)$ must satisfy. Graph both equations in Desmos and click their intersection, where the lines meet. The point gives you the coordinates, not necessarily the answer. If the question asks for a subtraction, keep its order: switching the coordinates changes the result.

Hints

Hint 1
A system needs one pair $(x,y)$ that makes both equations true. On a graph, what point belongs to both lines?
Hint 2
At an intersection, the coordinates are written $(x,y)$ : $x$ comes first and $y$ comes second. Label each coordinate before putting it into the subtraction the question asks for.

Step-by-step

Read the intersection in Desmos
Step 1
Graph the first equation
Type $y=2x+1$ . Desmos draws a line whose points make the first equation true. You still need a point that makes the second equation true too.
Step 2
Find the point shared by both lines
Add $4x-y=5$ as written. Click the intersection, where the lines meet. Desmos shows $(3,7)$ . Because that point is on both lines, it solves the system: $x=3$ and $y=7$ .
Step 3
Calculate the requested difference
The question asks for $y-x$ , not either coordinate alone. Put $y$ first, then subtract $x$ by typing $7-3$ in Desmos. It shows $4$ :
$\begin{aligned}y-x&=7-3\\[1.4em]&=4.\end{aligned}$
So the value of $y-x$ is $4$ . Choice A.

Question 534·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this