A system of linear equations with two variables can be expressed in a general form:

*ax + by = p*

*cx + dy = q*

Two variable linear equations can be solved using matrices or by using the elimination method.

Since the elimination method is an easy approach, here an example is presented.

Example:

Find solution set for given set of linear equations:

2x -2y = 8 … (1)

1x + 1y = 1 … (2)

Solution:

By multiplying equation 2 with 2 and adding both equations:

2x – 2y = 8

2x + 2 = 2

We obtain:

4x = 10

or x = 5/2

or x = 2.5

Putting value of x in first equation:

2 (2.5) – 2 y = 8

2y = 5 – 8

y = -3 / 2 = -1.5

So our solution set is:

(2.5, -1.5)

By putting above values in our equations we can easily verify.

Let’s put values in first equation:

2x – 2y = 8;

L.H.S = 2 (2.5) – 2(-1.5)

= 5 + 3

= 8

Since LHS = RHS our S.S is valid

MCQs below involve linear equations with four possible solution sets. Solve the equations and find the answer.

*2x – y = -43x – y = -2*

- (10, 52)
- (1, -6)
- (2, 8)
- (4, 3.78)

Correct answer: 3. (2, 8)

*5x + 2y = 53x + 6y = 6*

- (0.75, 0.625)
- (1.8, 7.6)
- (2, 9)
- (3.5, 11.8)

*10x + 5y = -27x + 4y = -4*

- (9.312, -33.8)
- (12, -33.8)
- (1.2, -12)
- (2.4, -5.2)

Correct answer: 4. (2.4, -5.2)

*3x + 3y = 82x + 9y = 1*

- (5.8, 9.2)
- (3.2, -0.6)
- (2, 4)
- (1, 0.22)

Correct answer: 2. (3.2, -0.6)

*8x + 3y = 22x + 3y = 5*

- (-0.25, 15)
- (-0.5, 2)
- (-1, -0.945)
- (4, 3.78)

Correct answer: 2. (-0.5, 2)