SOLVING WORD PROBLEMS USING SUBSTITUTION METHOD

In this section, you will learn how to solve linear linear equations in two variables using the concept substitution.

We use the following steps to solve a system of linear equations.

Problems

Problem 1 :

Solve 2x  + 3y  =  11 and 2x - 4y  =  -24 and hence find the value of "m" for which y  =  mx + 3.

Solution :

2x + 3y  =  11 ----------- (1)

2x - 4y  =  -24 ----------- (2)

Step 1 :

Find the value of one variable in terms of other variable

3y  =  11 - 2 x

y  =  (11 - 2 x)/3

Let us apply the value of y in (2),

2x - 4(11 - 2x)/3  =  -24

14x - 44  =  -24 (3)

14x - 44  =  -72

 14x  =  -72 + 44

14x  =  - 28

Divide 14 on both sides, we get

x  =  -2

Substitute x  =  -2  in the equation y  =  (11 - 2 x)/3

y  =  [11 - 2(-2)]/3

y  =  15/3

y = 5

Now we have to apply these values in the equation

y   =  m x + 3 

5  =  m (-2) + 3

5  =  -2 m + 3

-2m  =  2

-2 m  =  2

m  =  2/(-2)

m  =  -1

Problem 2 :

Form the pair of linear equations of the following problems and find their solution by substitution method.

(i) The difference between two numbers is 26 and one number is three times the other. Find them

Solution :

Let the two numbers are "x" and "y"

Difference between two number is 26

x - y  =  26 -------- (1)

One number is three times the other

x  =  3 y -------- (2)

Let us apply (2) in (1)

3 y - y  =  26

2 y  =  26

Divide by 2 on both sides, we get

y  =  13

By applying the value of y in (2), we get

x  =  3 (13)

x  =  39

So, required two numbers are 39 and 13.

Problem 3 :

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them

Solution :

Let the two supplementary angles are "x" and "y"

Sum of these two angles is 180

 x + y  =  180 -----(1)

the larger angle exceeds the smaller by 18

 x  =  y + 18 -----(2)

Now,we are going to apply the value of x in the first equation

y + 18 + y  =  180

2y  =  180 - 18

2y  =  162

y  =  162/2

 y  =  81

 x  =  81 + 18

 x  =  99

So, two supplementary angles are 99 and 81.

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