Foundations
Exactly One Solution to a System on the SAT: Desmos Walkthrough
Graph both equations as lines. If they cross there is one solution; if they run parallel and never meet, there are none.
This is a Foundations lesson: the core Desmos moves (graphing both sides, plotting points, reading intersections) that every other technique in the course builds on.
Take this lesson interactivelyA real SAT-style question
How many solutions does the given system of equations have?
A
Exactly one
B
Exactly two
C
Infinitely many
D
Zero
How to solve it in Desmos, step by step
The idea
Graph both equations as lines. If the two lines are parallel and never cross, the system has zero solutions.
- 1
Step 1
Type the first equation exactly as written. Desmos draws it as a straight line.Type in Desmos
- 2
Step 2
Type the second equation on the next line. Desmos draws it as a second straight line.Type in Desmos
- 3
Step 3
Look at the two lines on the graph. They run parallel and never meet, so Desmos shows no gray intersection dot anywhere. No crossing point means the answer is D, Zero.
The answer is D.
Zero
Now you try one
Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.
How many solutions does the given system of equations have?
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