Substitution technique of linear equations - linear algebra, Mathematics

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What is Substitution Technique of Linear Equations?

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james 2/12/2013 3:09:01 AM To demonstrate Substitution technique, consider the system of two equations (i). and (ii) reproduced underneath as: 2x - 3y = 8 ........ (i). 3x + 4y = -5 ...... (ii). The solution of such system can be acquired by 1) Solving one of the equations for one variable in terms of other variable; 2) Substituting this value into the another equation(s) thereby getting an equation along with one unknown only 3) at last Solving this equation for its single variable 4) Substituting this value into any one of the two original equations as like to receive the value of the second variable Step 1 Solve equation (i) for variable x in terms of y 2x - 3y = 8 x= 4 + (3/2) y (iii) Step 2 Substitute this value of x into equation (ii). And get an equation in y only 3x + 4y = -5 3 (4 + (3/2) y) + 4y = -5 8 ½ y = - 17 ....... (iv) Step 3 Solve the equation (iv). For y 8½y = -17 y = -2 Step 4 Substitute this value of y into equation (i) or (iii) and get the value of x 2x - 3y = 8 2x - 3(-2) = 8 x = 1

james

2/12/2013 3:09:01 AM

To demonstrate Substitution technique, consider the system of two equations (i). and (ii) reproduced underneath as:

2x - 3y = 8 ........ (i).

3x + 4y = -5 ...... (ii).

The solution of such system can be acquired by

1) Solving one of the equations for one variable in terms of other variable;

2) Substituting this value into the another equation(s) thereby getting an equation along with one unknown only

3) at last Solving this equation for its single variable

4) Substituting this value into any one of the two original equations as like to receive the value of the second variable

Step 1

Solve equation (i) for variable x in terms of y

2x - 3y = 8

x= 4 + (3/2) y (iii)

Step 2

Substitute this value of x into equation (ii). And get an equation in y only

3x + 4y = -5

3 (4 + (3/2) y) + 4y = -5

8 ½ y = - 17 ....... (iv)

Step 3

Solve the equation (iv). For y

8½y = -17

y = -2

Step 4

Substitute this value of y into equation (i) or (iii) and get the value of x

2x - 3y = 8

2x - 3(-2) = 8

x = 1

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