SOLVING SYSTEM OF EQUATIONS BY SUBSTITUTION EXAMPLES

Example 1 :

Solve the following system of equations by substitution method.

5x - 3y - 8 = 0  and  2x - 3y - 5 = 0  

Solution :

5x - 3y - 8  =  0  ------(1)

2x - 3y - 5  =  0  ------(2)

Step 1 :

Solve (1) for 3y. 

5x - 3y - 8  =  0

Add 8 to each side.

5x - 3y  =  8

Subtract 5x from each side.

-3y  =  8 - 5x

Multiply each side by (-1).

3y  =  5x - 8 -----(3)

Step 2 : 

Substitute (5x - 8) for y into (2). 

(2)-----> 2x - (5x - 8) - 5  =  0

2x - 5x + 8 - 5  =  0

-3x + 3  =  0

Subtract 3 from each side. 

-3x  =  -3

Divide each side (-3).

x  =  1

Step 3 :

Substitute 1 for x into (3).

(3)-----> 3y  =  5(1) - 8

3y  =  5 - 8

3y  =  -3

Divide each side by 3.

y  =  -1

Therefore, the solution is 

(x, y)  =  (1, -1)

Example 2 :

Solve the following system of equations by substitution method.

x - 3y - 11 = 0  and  5x + y - 7 = 0

Solution :

x - 3y - 11  =  0 -----(1) 

5x + y - 7  =  0 -----(2) 

Step 1 :

Solve (1) for x. 

x - 3y - 11  =  0

Add 11 to each side.

x - 3y  =  11

Add 3y to each side.

x  =  3y + 11 -----(3)

Step 2 : 

Substitute (3y + 11) for y into (2). 

(2)-----> 5(3y + 11) + y - 7  =  0

15y + 55 + y - 7  =  0

16y + 48  =  0

Subtract 48 from each side. 

16y  =  -48

Divide each side 16.

y  =  -3

Step 3 :

Substitute -3 for y into (3).

(3)-----> x  =  3(-3) + 11

x  =  -9 + 11

x  =  2

Therefore, the solution is 

(x, y)  =  (2, -3)

Example 3 :

Solve the following system of equations by substitution method.

y = 6x - 11  and  2x + 3y = 7

Solution :

y  =  6x - 11 -----(1)

2x + 3y  =  7 -----(2)

Step 1 :

From (1), substitute (6x - 11) for y in (2).

(2)-----> 2x + 3(6x - 11)  =  7

Simplify.

2x + 18x - 33  =  7

20x - 33  =  7

Add 33 to each side. 

20x  =  40

Divide each side by 20.

x  =  2

Step 2 : 

Substitute 2 for x into (1). 

(1)-----> y  =  6(2) - 11

 y  =  12 - 11

y  =  1

Therefore, the solution is 

(x, y)  =  (2, 1)

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