Linear System Calculator

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A linear equation is a first degree algebraic equation which consists of variables and constants. The linear system calculator is used to solve for the variable. If there are two unknown variables then the system of equations can be solved by using Substitution method or Elimination method or graphing method.

Example 1: Solve for x in 2x + 7 = 15

 Here the unknown variable is x

Any operation that is performed should be done on both sides of the equation.

Step 1: Add -7 on both sides of the given equation

                                    2x + 7 – 7 = 15 – 7

                                     2x = 8

Step 2: Divide by 2 on both sides of the given equation

                                    2x / 2 = 8 / 2

                                     x = 4

CHECK:     2x + 7 = 15

                   2(4) + 7 = 15

                   8 + 7 = 15

                     15 = 15

Hence the result is x= 4



Example 2: Solve the system of equations x + y = 24 and 2x – y = 3

Here there are two unknown variables x and y

Substitution Method:

x + y = 24 => y = 24 – x

Substitute y = 24 – x in the second equation 2x – y = 3

                                                                        2x – (24 – x) = 3

                                                                        2x – 24 + x = 3

                                                                        3x – 24 = 3

                                                                        3x = 27

                                                                         x = 9

Substitute x = 9 in the equation y = 24 – x

                                                   y = 24 – 9

                                                    y = 15

Solution set is (9, 15)

Elimination method:

x  +  y = 24

2x – y = 3

3x       = 27

   x     = 9

Substitute x = 9 in x + y = 24

                               9 + y = 24

                                     y = 24 – 9

                                      y = 15

Solution set is (9, 15)



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