| --- |
| source: ncert |
| topic: algebra |
| class_level: class_9 |
| chapter: ch4 |
| difficulty: beginner |
| --- |
| |
| Class 9 | Ch4: Linear Equations in Two Variables |
| FORM: ax+by+c=0 where a,b are not both zero. x and y are variables. |
| A linear equation in two variables has INFINITELY MANY solutions. |
| Each solution is an ordered pair (x,y) that satisfies the equation. |
| GRAPH OF LINEAR EQUATION IN TWO VARIABLES: |
| Graph is always a STRAIGHT LINE. |
| To draw: find at least 2 solutions (3 recommended to verify). |
| For 2x+3y=12: |
| x=0: 3y=12, y=4. Point (0,4). |
| y=0: 2x=12, x=6. Point (6,0). |
| x=3: 6+3y=12, y=2. Point (3,2). All 3 collinear confirms straight line. |
| X-INTERCEPT: point where line crosses x-axis. Set y=0 and solve for x. |
| Y-INTERCEPT: point where line crosses y-axis. Set x=0 and solve for y. |
| EQUATIONS OF SPECIAL LINES: |
| x=a: vertical line parallel to y-axis, passing through (a,0). |
| y=b: horizontal line parallel to x-axis, passing through (0,b). |
| y=x: line through origin, bisects I and III quadrants. |
| EXPRESSING WORD PROBLEMS AS LINEAR EQUATIONS: |
| "Cost of x pencils at 2 each and y pens at 5 each is 50": 2x+5y=50. |
| SOLVED EXAMPLES: |
| Example 1: Draw graph of 2x+3y=12. Find x and y intercepts. |
| y-intercept (x=0): y=4. So (0,4). |
| x-intercept (y=0): x=6. So (6,0). |
| Plot (0,4), (6,0), (3,2). Join them. |
| Example 2: Find 3 solutions of x+2y=8. |
| (0,4), (8,0), (2,3). Verify: 0+8=8, 8+0=8, 2+6=8. All correct. |
| COMMON MISTAKES: |
| A linear equation in two variables has infinite solutions (not just 2 or 3). |
| Every point on the graph is a solution. Every solution gives a point on the graph. |
| Graph of x=3 is a VERTICAL line (not a point on x-axis). |
