LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

INTRODUCTION OF SIMULTANEOUS LINEAR EQUATION

** ****Simultaneous Linear Equations –**

**As we all know, from the previous lesson about linear
equation and inequation, now we will learn about Simultaneous
Linear Equations. **

**A linear equation in two variables
(say, x & y) contains the variables in the first
degree and in separate terms. The general
form of such an equation is ax + by + 2 = 0, where a, b, & c are real
numbers and a & b are nonzero numbers.**

** y**

**Examples.) 2x – 5y =
7 &
5x + ------ + 3 = 0 are linear
equations in **

** 2**

**’x’ & ‘y’ , however 5xy = 9 is not a**

**linear equation because ‘x’ & ‘y’ are not contained in
separate terms.**

**Simultaneous Linear Equations –**

**If two linear equations in ‘x’ & ‘y’ are satisfied by
the same values of ‘x’ & ‘y’ then the equations are called simultaneous
linear equations. The general form of such equations is ax + by + c = 0 and px
+ qy + r = 0.**

**Example.) The equations x + 2y = 5 and 2x + y = 4 are
satisfied by the values x = 1, y =2. Therefore, x + 2y = 5 and 2x + y = 4 are
simultaneous linear equations and their solution is x = 1, y = 2. **

**To find a solution to simultaneous linear equations, we must
find a pair of values of the variables that satisfy both the equations. There are
two ways of doing this –**

**1) By Substitution
2) By Elimination**

__Substitution
Method –__

**There are some steps of substitution method are given below
– **

__Step.1)__ Using one of
the equations write ‘y’ in terms of ‘x’ or ‘x’ in terms of ‘y’ and the constant.

__Step.2)__ Substitute the expression for ‘y’ or ‘x’ in the
second equation.

__Step.3)__ Solve the resulting linear equations in ‘x’ or ‘y’.

__Step.4)__ Substitute the value of ‘x’ or ‘y’ in either of the
equations

__Step.5)__ Solve the resulting linear equations in ‘y’ or ‘x’

__Step.6)__ Verify the correctness of the solution by
substituting the values of ‘x’ & ‘y’ in the given equations.

__Elimination Method –__

**This method is also called the addition
subtraction method **

__Step.1)__
Decide which variable will be easier to eliminate, try to avoid fractions

__Step.2)__
Multiply one or both the equations by suitable numbers to ensure that the
coefficients of the variable to be eliminated are the same in both the
equations.

__Step.3)__ Add
or subtract the resulting equations to eliminate the variable

__Step.4)__ Solve
the resulting equation in one variable

__Step.5)__
Substitute the value of the variable obtained in step. 4in either of the given
equations.

__Step.6)__ Solve
the resulting equation.

__Step.7)__
Verify the correctness of the solution by substituting the values of the
variables in the given equations.