How many solutions does a linear equation in two variables have?

A linear equation in two variables (ax + by + c = 0) has infinitely many solutions. This is because for every value you substitute for x, you get a corresponding y value. The graph of the equation is a straight line, and every point on that infinite line represents a solution. For example, 2x + y = 6 is satisfied by (0,6), (1,4), (2,2), (3,0), (−1,8)… infinitely many pairs.

What does the graph of x = 3 look like?

The equation x = 3 means x is always 3, but y can be any value. So its solutions are (3, 0), (3, 1), (3, −2), (3, 5)… all having x = 3. When plotted, this gives a vertical straight line parallel to the Y-axis, passing through the point (3, 0) on the X-axis.

What is the standard form of a linear equation in two variables?

The standard form is ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. Any linear equation can be written in this form. For example, 3x = 2y − 5 can be rewritten as 3x − 2y + 5 = 0 (a=3, b=−2, c=5).

Graphical Method

Linear Equations in Two Variables • Class 9 Mathematics • NCERT • CBSE

A linear equation in two variables is of the form ax + by + c = 0, where a, b, c are real numbers. Every linear equation in two variables has infinitely many solutions. Its graph is always a straight line. Any point on the line satisfies the equation.

Key Formulas

ax + by + c = 0
y = (c − ax)/b

Frequently Asked Questions

How many solutions does a linear equation in two variables have?: A linear equation in two variables (ax + by + c = 0) has infinitely many solutions. This is because for every value you substitute for x, you get a corresponding y value. The graph of the equation is a straight line, and every point on that infinite line represents a solution. For example, 2x + y = 6 is satisfied by (0,6), (1,4), (2,2), (3,0), (−1,8)… infinitely many pairs.
What does the graph of x = 3 look like?: The equation x = 3 means x is always 3, but y can be any value. So its solutions are (3, 0), (3, 1), (3, −2), (3, 5)… all having x = 3. When plotted, this gives a vertical straight line parallel to the Y-axis, passing through the point (3, 0) on the X-axis.
What is the standard form of a linear equation in two variables?: The standard form is ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. Any linear equation can be written in this form. For example, 3x = 2y − 5 can be rewritten as 3x − 2y + 5 = 0 (a=3, b=−2, c=5).

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