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Solve by Graphing

Identifying Points on Coincident Lines on the SAT: Desmos Walkthrough

Learn to graph two equations that secretly describe the same line and read off which given point sits on both of them.

This lesson solves by graphing: turn the equation into curves, then read intersections, vertices, or tangency straight off the Desmos graph.

Take this lesson interactively

A real SAT-style question

7 2 x + 6 y = 25

5 2 x + 6 y = 23

The solution to the given system of equations is (x,y). What is the value of 17 2 x + 18 y ?

A

2

B

3

C

48

D

71

How to solve it in Desmos, step by step

The idea

Graph both equations, click the gray dot where they cross to read the solution, then type the target expression with those values so Desmos computes it.

  1. 1

    Step 1

    Type the first equation. Desmos draws a line.

    Type in Desmos

    72x+6y=25\frac{7}{2}x+6y=25
  2. 2

    Step 2

    Type the second equation on the next line. Desmos draws a second line.

    Type in Desmos

    52x+6y=23\frac{5}{2}x+6y=23
  3. 3

    Step 3

    Click the gray dot where the two lines cross. Desmos labels it as the point 2 comma 3, so x is 2 and y is 3.
  4. 4

    Step 4

    Type the target expression with 2 in place of x and 3 in place of y. Desmos shows 71, which is choice D.

    Type in Desmos

    172(2)+18(3)\frac{17}{2}\left(2\right)+18\left(3\right)

The answer is D.

71

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

92x+4y=30\frac{9}{2}x + 4y = 30
32x+4y=18\frac{3}{2}x + 4y = 18

The solution to the given system of equations is (x,y)(x, y). What is the value of 212x+12y\frac{21}{2}x + 12y?

Practice this with a live Desmos calculator

The interactive version of this lesson builds the Desmos graph up step by step as you click through, with a live calculator you can type into and your progress saved.

Open the interactive lesson

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