Systems of Simultaneous Linear Equations

 You may recall earlier learning on one variable and applying them for solving word problems. If a and b are two real numbers such that a 0 and x is a variable, then as we have learnt that an equation of the form ax = b or, ax + b = 0 is called a linear equation in one variable. Recall that a value of the variable which satisfies a given linear equation in one variable is known as its solution similar two variables also. Moving forward it covers about systems of linear equations in two variables, solution of a system of linear equations in two variables and graphical and algebraic methods of solving a system of linear equations in two variables. Systems of Simultaneous Linear Equations Definition: A pair of linear equations in two variables is said to form a system of simultaneous linear equations.
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 Example: Show that x = 3, y = 5 is not a solution of the system of simultaneous linear equations       2x + 7y = 11       x - 3y = 5 Solution: The given system of equations is       2x + 7y = 11 ... (i)       x - 3y = 5 ... (ii) Putting x = 3, y = 5 in equation (i), you have      LHS = 2 * 3 + 7 * 5 = 6 + 35 = 41 RHS So, x = 3 and y = 5 do not satisfy equation (i). Putting x = 3 and y = 5 in equation (ii), you have      LHS =3 - 3 * 5 = -12 RHS So, x = 3 and y = 5 do not satisfy equation (ii). Hence, x = 3, y = 5 is not a solution of the given system of equations.

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