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MEAP Preparation - Grade 7 Mathematics
2.92 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: 9x + 10 = 19
Two Variable Linear Equation
One Variable Linear Equation
Non-linear Equation

Q 2: 17x + 9 = 26 - y
Two Variable Linear Equation
Non-linear Equation
One Variable Linear Equation

Q 3: 7x2 + 9 = 16
Two Variable Linear Equation
Non-linear Equation
One Variable Linear Equation

Q 4: 7x + 8 = 15
Two Variable Linear Equation
One Variable Linear Equation
Non-linear Equation

Q 5: 7x + 10 = 27x - 30
Non-linear Equation
Two Variable Linear Equation
One Variable Linear Equation

Q 6: 8x2 + 9 = 17
One Variable Linear Equation
Two Variable Linear Equation
Non-linear Equation

Q 7: 9x3 + 7 = 16
One Variable Linear Equation
Non-linear Equation
Two Variable Linear Equation

Q 8: 15x + 15y = 10
Non-linear Equation
One Variable Linear Equation
Two Variable Linear Equation

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Question 10: This question is available to subscribers only!


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