Solve the following system of equations graphically:
2x + y = 6, 2x − y − 2 = 0.
Answer: The lines meet at (2, 2): x = 2, y = 2.
Step-by-step solution
Idea: Draw each line from a table of two or three points; the solution is the point common to both lines.
- 2x + y = 6:
1 markx 0 1 3 y 6 4 0 - 2x − y − 2 = 0, i.e. y = 2x − 2:
1 markx 0 1 3 y −2 0 4 - Plot both sets of points and draw the two lines (see the graph).1 mark
- They intersect at (2, 2). So x = 2, y = 2.1 mark
x = 2, y = 2.
Check: 2(2) + 2 = 6 ✓; 2(2) − 2 − 2 = 0 ✓.
Answer to write in the exam
2x + y = 6:
| x | 0 | 1 | 3 |
| y | 6 | 4 | 0 |
2x − y − 2 = 0:
| x | 0 | 1 | 3 |
| y | −2 | 0 | 4 |
Plotting, the lines intersect at (2, 2)
∴ x = 2, y = 2
Common mistakes that cost marks
- Rewriting 2x − y − 2 = 0 as y = −2x + 2 (sign error).
- Reading the crossing point as (2, 1) from a rough sketch.
How this can come in the exam
MCQ (1 mark)
The graphs of x + y = 6 and x − y = 2 intersect at
- (2, 4)
- (4, 2)
- (3, 3)
- (6, 0)
Show answer
(B) (4, 2)
Adding: 2x = 8 ⇒ x = 4, y = 2.
Try one yourself
Solve graphically: x + 2y = 4 and x − y = 1.
Show answer
Points (0, 2), (4, 0) and (1, 0), (3, 2): the lines meet at (2, 1).
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