# 9th Class Mathematics Linear Equations in Two Variables

Linear Equations in Two Variables

Category : 9th Class

Linear Equations in Two Variables

• Equation: A statement of equality of two algebraic expressions involving a variable is called an equation.

• Simple linear equation: An equation which contains only one variable of degree 1 is called a simple linear equation.

• Solution of an equation: The value of the variable, which when substituted in the given equation, makes the two sides L.H.S (Left Hand Side) and R.H.S (Right Hand Side) of the equation equal is called the solution of that equation.

• Transposition: Any term of an equation may be taken to the other side with a change in its sign. This process is called transposition.

• Cross multiplication: If $\frac{\operatorname{ax}+b}{\operatorname{cx}+d}=\frac{p}{q}$then q (ax + b) = p (cx + d). This process is called cross multiplication.

• Linear equation in one variable: An equation of the form ax + b = 0 or ax = c, is a linear equation in one variable x, where $a\ne 0$and a, b and c are real numbers.
• Solution of a linear equation in one variable: The value of the variable (x) for which both the sides of the equation become equal is said to be the solution of the equation.

Note: A solution is also called the ‘root’ of the equation.

• Linear equation in two variables:

(i) An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that 'a' and 'b' are not both zero, is called a linear equation in two variables.

(ii) A linear equation in two variables has infinitely many solutions.

(iii) The graph of every linear equation in two variables is a straight line.

(iv) x = 0 is the equation of Y-axis.

(v) y = 0 is the equation of X-axis.

(vi) The graph of x = a is a straight line parallel to the Y-axis.

(vii) The graph of y = a is a straight line parallel to the X-axis.

(viii) An equation of the type y = mx represents ‘a line passing through the origin.

(ix) Every point on the graph of a linear equation in two variables is a solution of the linear equation. Conversely, every solution of the linear equation is a point on the graph of the linear equation.

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##### Notes - Linear Equations in Two Variables

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