Linear Equations in Two Variables — Question 1
Back to all questionsGiven, linear equation y = 3x + 5
We know that,
y = 3x + 5 is a linear equation in two variables in the form of ax + by + c = 0
Substituting x = 0, in y = 3x + 5, we get :
⇒ y = 3(0) + 5 = 0 + 5 = 5.
∴ (0, 5) is one solution.
Substituting x = 1, in y = 3x + 5, we get :
⇒ y = 3(1) + 5 = 3 + 5 = 8.
∴ (1, 8) is another solution.
Substituting x = 2, in y = 3x + 5, we get :
⇒ y = 3(2) + 5 = 6 + 5 = 11.
∴ (2, 11) is another solution.
Clearly, for different values of x, we get different values of y.
Thus, y = 3x + 5 has infinitely many solutions.
Hence, Option (iii) is the correct answer.
Linear Equations in Two Variables — Interactive Study Guide
Infinite Solutions
A linear equation in two variables has infinitely many solutions. Each solution is a point on the line. The line extends forever in both directions.
Graphing Made Easy
- Rewrite as y = mx + c.
- Make a table: choose 3 values of x, calculate y for each.
- Plot the 3 points. If they’re collinear, draw the line.
Special Lines
y = 3: Horizontal line, 3 units above x-axis.
x = −2: Vertical line, 2 units left of y-axis.
y = x: Line at 45° through origin.
Quick Self-Check
- Is (2, 3) a solution of x + y = 5? (Yes: 2 + 3 = 5)
- Give 3 solutions of y = 2x. ((0,0), (1,2), (2,4))
- What is the equation of the x-axis? (y = 0)