Linear Equations in Two Variables (NCERT Ch. 4)

• Write equations of the form ax + by + c = 0 with real coefficients.
• Find solutions as ordered pairs (x, y) and plot them as points on the Cartesian plane.
• Recognise that a linear equation in two variables has infinitely many solutions.
• Graph a line from its equation using intercepts or a table of values.
• Model simple real situations (age, money, distance) as linear equations.

1. Standard form — ax + by + c = 0 where a, b are not both zero.
2. Solution — Any pair (x₀, y₀) satisfying the equation; e.g. 2x + 3y = 12 has (0, 4), (3, 2), (6, 0).
3. Graph — All solutions lie on one straight line.
4. Intercepts — x-intercept: set y = 0; y-intercept: set x = 0.
5. Infinitely many solutions — Every point on the line is a solution.
6. Real-life — Cost = 50x + 30y for x notebooks and y pens if prices are fixed.
7. NCERT Ex. 4.2 — Write four solutions of x + y = 7; plot them.
8. Checking — Substitute a pair into both sides to verify equality.

Verify whether (2, 3) is a solution of 3x + 2y = 12

LHS = 3(2) + 2(3) = 6 + 6 = 12 = RHS
Conclusion: (2, 3) is a solution.
Plot: point (2, 3) lies on the line 3x + 2y = 12.

• Plotting only one point and calling it the whole line.
• Confusing x and y when substituting into ax + by + c = 0.
• Thinking a linear equation has only one solution.
• Using non-linear graphs for equations like xy = 6 (not linear in two variables).

• Is (1, 2) a solution of x − y = 1?
• Write two solutions of 2x + y = 10.
• Find the y-intercept of 4x + 2y = 8.
• How many solutions does a non-degenerate linear equation have?

Open the Practice tab for graded questions on Linear Equations in Two Variables (NCERT Ch. 4).