Q1. Find two solutions of 2x + y = 8.
Let x = 0: 2(0) + y = 8 ⇒ y = 8 → (0, 8)
Let x = 4: 2(4) + y = 8 ⇒ y = 0 → (4, 0)
Both (0, 8) and (4, 0) are solutions.
Linear Equations in Two Variables — Class 9
One equation, two unknowns — infinitely many solutions, all lying on one straight line. Compute any solution instantly.
Linear equation in two variablesAn equation of the form ax + by + c = 0, where a and b are not both zero.
SolutionAny pair (x, y) that satisfies the equation. A linear equation in two variables has infinitely many solutions.
GraphEvery solution of ax + by + c = 0 is a point on a straight line, and every point on that line is a solution.
Solve-for-y calculator Interactive
Enter a, b, c and a value of x to find the matching y on the line ax + by + c = 0.
y = −(ax+c)/b—
Pick any x you like — a linear equation in two variables has infinitely many (x, y) solutions, all on one line.
Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| General form | ax + by + c = 0 |
| Solve for y | y = −(ax + c)/b |
| x-intercept (y=0) | x = −c/a |
Common mistakes & exam wins
- A linear equation in ONE variable has one solution; in TWO variables it has infinitely many.
- The easiest solutions to find are where x = 0 or y = 0.
- y = mx + c is a special case of ax + by + c = 0 (with b = −1... rearranged).
Frequently asked questions
How many solutions does a linear equation in two variables have?
Infinitely many — every point on the line it represents is a solution.
What is the graph of ax + by + c = 0?
A straight line; every solution of the equation is a point on that line.
How do you find the x-intercept of a line?
Set y = 0 and solve for x: x = −c/a.