Example 1 · level 1
Which of these points is a solution of 5x + 2y = 23?
- (6, −1)
- (5, −1)
- (−1, 5)
- (5, 0)
Show solution
- For (5, −1): 5 × 5 + 2 × (−1) = 25 + (−2) = 23. ✓
- The other points do not give the right-hand side.
Answer: (5, −1)
CLASS 9 MATHS · LINEAR EQUATIONS IN TWO VARIABLES
Solutions of linear equations in two variables
A point (p, q) is a solution of ax + by = c if a·p + b·q equals c. Each such equation has infinitely many solutions.
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Worked examples
Example 2 · level 2
If x = 1, y = 1 is a solution of kx + y = −4, find k.
Show solution
- 1k + 1 = −4
- 1k = −5
- k = −5.
Answer: -5
Example 3 · level 3
The line 3x + y = 6 crosses the x-axis at a point. What is its x-coordinate?
Show solution
- y = 0: 3x = 6 → x = 2.
- The point is (2, 0).
Answer: 2