Solution as Ordered Pair MCQs Quiz | Class 9
This quiz covers Class IX Mathematics (Code 041), Unit II: Algebra. The topic focuses on Linear Equations in Two Variables, specifically writing solutions as ordered pairs (x, y) and checking if a given point is a solution. Please attempt all questions and download your result PDF.
Understanding Solutions as Ordered Pairs
In Class 9 Mathematics, Unit II: Algebra covers Linear Equations in Two Variables. A key concept is understanding that a linear equation in two variables, such as ax + by + c = 0, has infinitely many solutions. These solutions are written as ordered pairs.
Key Concepts
- Ordered Pair (x, y): A solution is always written with the x-coordinate first and the y-coordinate second. For example, (2, 3) means x = 2 and y = 3.
- Checking a Solution: To check if a point (h, k) lies on the line of an equation, substitute x = h and y = k into the equation. If LHS = RHS, it is a solution.
- Finding Solutions: To find a solution, assign a numerical value to x (or y) and solve the resulting equation for the other variable.
- Graphing: Every solution (x, y) corresponds to a point on the line representing the equation.
Common Solution Methods
| Method | Description |
|---|---|
| Substitution | Put a value for x, calculate y. |
| Verification | Put given (x,y) into equation to check equality. |
| Zero Method | Put x=0 to find y-intercept, y=0 to find x-intercept. |
Quick Revision Points
- A linear equation in two variables has infinitely many solutions.
- The graph of every linear equation in two variables is a straight line.
- x = 0 is the equation of the y-axis; y = 0 is the equation of the x-axis.
- The graph of x = a is a straight line parallel to the y-axis.
- The graph of y = a is a straight line parallel to the x-axis.
Practice Questions
- Find two solutions for 2x + y = 7.
- Check if (1, 1) is a solution of 3x – 2y = 5.
- If x = 2, y = 1 is a solution of 2x + 3y = k, find k.
- Write the equation 5x = 2 in the form ax + by + c = 0.
- Find the value of y if x = -1 in equation x – y = 4.
