Question 339·Medium·Algebra

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The system of equations is

$4x - y = 7$

$x + 2y = 4$

The solution to the system is $(x, y)$ . What is the value of $2x - y$ ?

A system of equations gives two facts about the same $x$ and $y$ . If the question says the solution is $(x,y)$ but asks for another expression, graph both equations in Desmos and click their intersection. Then put both coordinates into the expression asked for. Watch its signs: changing subtraction to addition changes the answer.

Hints

Hint 1
The solution of a system is one pair $(x,y)$ that makes both equations true. Each equation graphs as a line. What does the point where those lines cross tell you?
Hint 2
An ordered pair lists $x$ first and $y$ second. After you click the crossing point, put each coordinate in its place in the expression the question asks for, keeping the minus sign.

Step-by-step

Graph the system, then evaluate
Step 1
Find the solution point
Type $4x-y=7$ and $x+2y=4$ on separate Desmos lines. Click their intersection, where the lines cross. Desmos shows $(2,1)$ , so $x=2$ and $y=1$ . That one point makes both equations true.
Step 2
Evaluate what the question asks for
The target is $2x-y$ , not either coordinate by itself. Type $2(2)-1$ on the next line; Desmos prints $3$ . So the value of $2x-y$ is $3$ . Choice C.

Question 339·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this