Cogito
Algebra 1 · Chapter 5 · Lesson 2
Solving Systems by Graphing
The crossing point is the answer.
11 problems · about 22 minutes · A-REI.C.6, A-REI.D.11
What this lesson teaches
The student solves a system graphically and classifies the number of solutions.
- The solution of a system is a point on both lines.
- Different slopes cross once; equal slopes are parallel or identical.
- Comparing slopes and intercepts settles the count before any drawing.
Warm Up
Straightforward practice. Get the method working first.
4 problemsSlopes 3 and 3, intercepts 1 and 4. How many solutions?
Answer 0
Why None.
Slopes 2 and 7. How many solutions?
Answer 1
Why Different slopes.
Slopes 5 and 5, intercepts 2 and 2. How many? Use 99 for infinitely many.
Answer 99
Why One line twice.
Slopes 5 and 5, intercepts 2 and 9. How many solutions?
Answer 0
Why Parallel.
Build It Up
The same ideas with more to keep track of.
3 problemsLines cross at (3, 8). What is x in the solution?
Answer 3
Why Read the point.
Sort each pair of lines by how many solutions the system has.
Answer Exactly one: Different slopes · None: Same slope, different intercept · Infinitely many: Same slope, same intercept
Why Compare slopes first, then intercepts.
Must a solution satisfy both equations? 1 for yes, 0 for no.
Answer 1
Why That is what a system means.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsy = x and y = 2x cross at which x?
Answer 0
Why x = 2x.
y = x + 1 and y = x + 1. How many? Use 99 for infinitely many.
Answer 99
Why Identical.
Different Slopes: Slopes 3 and 5. How many solutions?
Answer 1
Why One.
Parallel: Slopes 4 and 4, intercepts 1 and 6. How many solutions?
Answer 0
Why None.