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Introduction |
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A simple linear equation is a statement of equality between two algebraic expressions involving an unknown quantity called the variable. In a linear equation the power of the variable is always equal to 1. The two sides of an equation are called Left-Hand Side (LHS) and Right Hand Side (RHS). |
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Equations of condition |
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The two expressions (LHS and RHS) are equal only for a particular value of the variable (x). These equations are called equations of condition. An equation of condition is generally referred to as an equation. |
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Identical equations or identities |
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The two expressions (LHS and RHS) are always equal for any value we give to the variable. Equations that are true for any value of the variable are called identical equations or briefly an identity. |
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Solving linear equations |
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The process of finding the value of the unknown quantity for which the equation is true, is called solving the equation. The value so found is called the root or solution of the equation. |
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The process of solving a simple equation depends upon the following axioms:
Addition property, Subtraction property, Multiplication and division property. |
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Linear equations in two variables |
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An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear. |
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A linear equation in two variables is of the form ax + by = c,where 
A linear equation in two variables has infinitely many solutions. |
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Graphical representation of a Linear Equation in two variables |
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The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide.
The horizontal number line is called x-axis and the vertical number line is called y-axis
The point of intersection of the two number lines is called origin.
The two number lines together are called rectangular axes.
The position of a point with respect to the rectangular axes by means of a pair of numbers is called co-ordinates. |
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Graph of Linear Equation in one variable |
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ax + b = 0 is a linear equation in one variable.
The graph of x = a is a line parallel to y-axis at x=a. The graph of y=b is a line parallel to x-axis at y = b. |
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Summary |
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A linear equation of the form ax + by + c = 0 where a = 0, b
¹ 0 is called a linear equation in two variables.
An equation is called a Linear equation in one variable or an equation of degree one in one variable, if only a single variable with degree one occurs in the equation.
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