Many students who experienced a staggering blow with the complicated linear equations specially system of linear equations with fractions and it has been very difficult for them to overcome. Thats the reason, we came up with some simple tricks to solve these type of equations where students feel confident and solve questions at their own pace. In this section will help you to understand how to solve equations either with one unknown or with two unknowns.

Let us first number the equations as (1) and (2)

2x + y = 7 -------------------------------(1)

3 x - y = 3 -------------------------------(2)

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On adding (1) and (2), we get 5x = 10 [ since + y - y = 0 ]

x = 10/5

x = 2

Substituting x=2, in Equation (1), we get,

2(2) + y = 7

4 + y = 7

y = 7 - 4 = 3

=> y = 3

Hence the

Let us first number the equations. 3x + y = 10 ---------------------(1)

6x + 2y = -5 ---------------------(2)

Multiplying Equation (1) by 2, we get 2 ( 3x + y ) = 2 ( 10)

=> 6x + 2y = 20 ----------------------(3)

6x + 2y = -5 -----------------------(2)

(-) (-) (+)

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Subtracting (2) from (3), we get 0 = 25 , which is a false statement.

Hence the above

Hence there will be infinite number of common solutions.

Let us first number the equations . 3x + 2y = 10 ----------------------------(1)

6x + 4 y = 20 ---------------------------(2)

Multiplying Equation (1) by 2, we get, 2 ( 3x + 2y ) = 2 ( 10)

6x + 4y = 20 ----------------------------(3)

6x + 4y = 20 ---------------------------(2)

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Subtracting (2) from (3), we get 0 = 0, which is true.

This is true for any values of x.

Since the values of y depends on the values of x, there will be infinite number of values for x and the corresponding values of y.

Hence

a. 4x + 15 = -1

b. 5 + 3x = 11

2. Solve the following pairs of equations, write the common solution/solutions if any.

a. 3x + 5y = -2 ; 4x - y = 5

b. 4x + 3y = 10, 12 x + 9 y = 30.

c. 8x + 3y = 11, 16 x + 6y = 22.

The linear equation of one variable is of the form ax + b = 0, where a and b are real numbers and a is not equal to 0. This equation has one and only solution. (i.e) the value of the variable x is unique.

Solving two step linear equations:

For any given linear equation of the form ax + b = 0,

Step 1: Subtracting b from both sides,

ax + b - b = 0 - b [ since b - b = 0 ]

=> ax = -b

Step 2: Dividing by a on both sides.

=> $ \frac{ax}{a}$ = $\frac{-b}{a}$

=> x = -$\frac{b}{a}$

Hence the final solution is x = - b/a

Example : solve 3x + 12 = 0

solution: Comparing this with the general equation ax + b = 0,

we get a = 3, b = 12

Therefore the solution ,

x = - $\frac{b}{a}$ = - $\frac{12}{3}$ = - 4