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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation1.16 Linear and Non-Linear Equations

 Linear Equations An equation in which the highest index of the variables present is one, is called a "linear equation". An equation with one variable and of first order (i.e., its highest power is one) is called a Linear equation. It has only one solution and is also called the 'root' of the given equation. Linear Equations with One Variable: Examples: x + 8 = 10 6x - 3 = 2x + 9 6x - 3 = 2x + 9 can be simplified as 4x = 12 Linear Equations with Two Variables: Examples: x + y = 20 In above example, there are two variables x and y, but the exponents of the variables are only one. Therefore, the equation x+y=20 is a linear equation in two variables. a + 4by = 15 Linear Equations with Three Variable : Examples: x + y + z = 67 2a + 5b + 3c = 34 Non-linear Equations Equations that have indexes are higher than 1 are called non-linear equations. Examples: 63 - 7x - 3 = 0 x4 - 5x2 = 5 Directions: Identify the type of equation given in each question. Also write at least 5 examples of linear and non-linear equations.
 Q 1: 15x + 15y = 10One Variable Linear EquationTwo Variable Linear EquationNon-linear Equation Q 2: 27x4 - 15 = 12Non-linear EquationTwo Variable Linear EquationOne Variable Linear Equation Q 3: 9x3 + 7 = 16One Variable Linear EquationNon-linear EquationTwo Variable Linear Equation Q 4: 7x + 10 = 27x - 30Non-linear EquationTwo Variable Linear EquationOne Variable Linear Equation Q 5: 8x2 + 9 = 17One Variable Linear EquationTwo Variable Linear EquationNon-linear Equation Q 6: 7x + 8 = 15Non-linear EquationTwo Variable Linear EquationOne Variable Linear Equation Q 7: 9x + 10 = 19Two Variable Linear EquationOne Variable Linear EquationNon-linear Equation Q 8: 17x + 9 = 26 - yTwo Variable Linear EquationOne Variable Linear EquationNon-linear Equation Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!