SOLVING SYSTEM OF EQUATIONS BY SUBSTITUTION

Example 1 :

Solve :

x + y = 5

2x + 3y = 5

Solution :

x + y = 5 ----(1)

2x + 3y = 5 ----(2)

Step 1 :

Solve (1) for y.

x + y = 5

Subtract x from each side.

y = 5 - x ----(3)

Step 2 :

Substitute (5 - x) for y into (2).

2x + 3(5 - x) = 5

2x + 15 - 3x = 5

15 - x = 5

Subtract 15 from each side.

-x = -10

Multiply each side by (-1).

x = 10

Step 3 :

Substitute 10 for x into (3).

y = 5 - 10

y = -5

Therefore, the solution is

(x, y) = (10, -5)

Example 2 :

Solve :

2x + 5y = 12

4x - y = 2

Solution :

2x + 5y = 12 ----(1)

4x - y = 2 ----(2)

Step 1 :

Solve (2) for y. 

4x - y = 2

Subtract 4x from each side.

-y = 2 - 4x

Multiply each side by (-1).

y = 4x - 2 ----(3)

Step 2 :

Substitute (4x - 2) for y into (1).

2x + 5(4x - 2) = 12

2x + 20x - 10 = 12

22x - 10 = 12

Add 10 to each side.

22x = 22

Divide each side by 22.

x = 1

Step 3 :

Substitute 1 for x into (3).

y = 4(1) - 2

y = 4 - 2

y = 2

Therefore, the solution is

(x, y) = (1, 2)

Example 3 :

Solve :

x + y - 4 = 0

2x - 3y - 18 = 0

Solution :

x + y - 4 = 0 ----(1)

2x - 3y - 18 = 0 ----(2)

Step 1 :

Solve (1) for x.

x + y - 4 = 0

Add 4 to each side.

x + y = 4

Subtract y from each side.

x = 4 - y ----(3)

Step 2 :

Substitute (4 - y) for x into (2).

2(4 - y) - 3y - 18 = 0

8 - 2y - 3y - 18 = 0

-5y - 10 = 0

Add 10 to each side.

-5y = 10

Divide each side by -5.

y = -2

Step 3 :

Substitute -2 for y into (3).

x = 4 - (-2)

x = 4 + 2

x = 6

Therefore, the solution is

(x, y) = (6, -2)

Example 4 :

Solve :

3x + 5y = - 2

2x - y = 3

Solution :

3x + 5y = -2 ----(1)

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

Step 1 :

Solve (2) for y.

2x - y = 3

Subtract 2x from each side.

-y = 3 - 2x

Multiply each side by (-1).

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

Step 2 :

Substitute (2x - 3) for x into (1).

3x + 5(2x - 3) = -2

3x + 10x - 15 = -2

13x - 15 = -2

Add 15 to each side.

13x = 13

Divide each side by 13.

x = 1

Step 3 :

Substitute 1 for x into (3).

y = 2(1) - 3

y = 2 - 3

y = -1

Therefore, the solution is

(x, y) = (1, -1)

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.