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Linear Equation in two variables
In this section we will discuss Linear Equation in two variables and different ways of solving it. Linear equation of the form ax + by + c = 0 or ax + by = c, where a, b and c are coefficient of x and y respectively and they are real numbers, 'a' is not equal to zero (a≠0) ,'b' is not equal to zero(b ≠ 0) and x and y are variables , is called a Linear equations in two variables. Example 1 : 2x + 3y  4 = 0 Here, a = 2 ; b = 3 and c = 4. Example 2 : x + y = 0 Here, a = 1 ; b = 1 and c = 0 A pair of linear equation in two variables is said to form a system of simultaneous linear equation. The values of x and y are the solution of the given equation. These values satisfies the given equation. Consistent : If there is at least one solution then the equations are consistent. In –consistent : If there is no solution then the equations are inconsistent. If the two lines are a _{1} x + b _{1} y + c _{1} = 0 and a _{2} x + b _{2} y + c _{2} = 0 then
Example 1: For what value of k will the equations x + 2y + 7 = 0; 2x + ky + 14 = 0 represent the coincident line. Solution : For coincident lines we have, ⇒ 1 / 2 = 2 / k = 7 / 14 ⇒ 1 /2 = 2 / k ∴ k = 4 There are 4 ways to solve the linear equations. Linear equation in two variables • Solving linear equation by graphical method. • Substitution method. • Solving system of equation by elimination method • Cross multiplication method or Cramer’s rule
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