ALGEBRAIC SOLUTION

1.  SUBSTITUTION

 Example:

Given:

-x + 6y = 4            (1)

2x – 9y = -5         (2)

Solution:

From (1), solve for x in terms of y

x = 6y - 4              (3) → substitute to (2)

2(6y - 4) – 9y = -5

12y - 8 – 9y = -5

3y = -5 + 8

3y = 3

y = 1            → substitute to (3)

x = 6(1) – 4

x = 2

Checking:

-x + 6y = 4

-(2) + 6(1) = 4

-2 + 6 = 4

4 = 4

2(2) – 9(1) = -5

4 – 9 = -5

-5 = -5

ANSWER: {(2, 1)}

2.  ELIMINATION

 Example:

Given:

3x– 2y = 1          (1)

2x + y = 10        (2)

Solution:

           3x – 2y = 1

2 [2x + y = 10] → 4x + 2y = 20

                                   7x         = 21

x = 3      → substitute to (1) or (2)

3(3) – 2y = 1

9 – 2y = 1

-2y = 1 – 9

-2y = -8

y = 4

2(3) + y = 10

6 + y = 10

y = 10 – 6

y = 4

Checking:

3(3) -2(4) = 1

9 – 8 = 1

1 = 1

2x + y = 10

2(3) + (4) = 10

6 + 4 = 10

10 = 10

ANSWER: {(3, 4)}