Solving Systems of Linear Equations
9-1The Graphing Method
Overview
Graph both lines; the solution is their intersection point.
Key ideas
- One intersection → one solution.
- Parallel lines → no solution.
- Same line → infinitely many solutions.
Worked examples
Example 1
Problem. Solve by graphing: y = x + 1 and y = −x + 5.
Solution. Lines meet at (2, 3).
Practice
Try each one. Click Show answer when ready.
- 1.
y = x and y = 4 intersect at?
- 2.
y = 2x and y = 2x + 1?
- 3.
y = x and y = x?
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve by graphing: y = 2x + 1 and y = −x + 4.
- 2.
Solve by graphing: x + y = 5 and 2x − y = 1.