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 = -4
3x – y = -2

  1. (10, 52)
  2. (1, -6)
  3. (2, 8)
  4. (4, 3.78)

Correct answer: 3. (2, 8)


5x + 2y = 5
3x + 6y = 6

  1. (0.75, 0.625)
  2. (1.8, 7.6)
  3. (2, 9)
  4. (3.5, 11.8)

10x + 5y = -2
7x + 4y = -4

  1. (9.312, -33.8)
  2. (12, -33.8)
  3. (1.2, -12)
  4. (2.4, -5.2)

Correct answer: 4. (2.4, -5.2)


3x + 3y = 8
2x + 9y = 1

  1. (5.8, 9.2)
  2. (3.2, -0.6)
  3. (2, 4)
  4. (1, 0.22)

Correct answer: 2. (3.2, -0.6)


8x + 3y = 2
2x + 3y = 5

  1. (-0.25, 15)
  2. (-0.5, 2)
  3. (-1, -0.945)
  4. (4, 3.78)

Correct answer: 2. (-0.5, 2)