Question 334·Easy·Algebra

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3x - y = 7 \\[1.4em] x + y = 5

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

A system of equations gives two equations that must hold for the same $x$ and $y$ . Graph both in Desmos and click their intersection, the point that satisfies both. Then use its coordinates in the expression the question actually asks for. Find the shared point, then evaluate the target.

Hints

Hint 1
An intersection is where two graphed lines cross. Its coordinates make both equations true, so type the equations as written and click that point rather than estimating coordinates from the grid.
Hint 2
In an ordered pair $(x,y)$ , the first coordinate is $x$ and the second is $y$ . Once you have both, put them into $x+2y$ . What must you multiply by $2$ ?

Step-by-step

Graph the system in Desmos
Step 1
Find the point that solves both equations
Type $3x-y=7$ and $x+y=5$ on separate Desmos lines. Click the intersection, where the lines cross; Desmos shows $(3,2)$ . Its coordinates make both equations true, so $x=3$ and $y=2$ .
Step 2
Evaluate what the question asks for
The requested expression is $x+2y$ , not the $x+y$ in the second equation. Put in $x=3$ and $y=2$ : type $3+2(2)$ on a new Desmos line. It prints $7$ , so the value of $x+2y$ is $7$ . Choice D.

Question 334·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this