Learn it
A system of equations is two or more equations with the same variables. A solution makes every equation true. On a graph, it is the point where the lines intersect.
- Lines cross once → one solution.
- Parallel lines (same slope, different intercepts) → no solution.
- The same line → infinitely many solutions.
Worked examples
Example 1
Solve by graphing: y = x + 1 and y = −x + 5.
- Line 1 passes (0, 1), (2, 3)
- Line 2 passes (0, 5), (2, 3)
- They meet at (2, 3). Check: 3 = 2 + 1 and 3 = −2 + 5
Answer: (2, 3)
Example 2
How many solutions: y = 2x + 3 and y = 2x − 4?
- Same slope 2, different intercepts
- The lines are parallel
Answer: No solution
Practice
Try these on paper first, then check your work.
- Is (1, 4) a solution of y = 3x + 1 and y = x + 3?
- y = x and y = −x meet where?
- y = 4x − 1 and 2y = 8x − 2
- y = 2 and x = −3 meet where?
Show the answer key
- Yes
- (0, 0)
- Infinitely many
- (−3, 2)