Simultaneous linear equation Solve the following equations:

a. 3x + 5y = 8 ,

4x – 3y = 1

b. 6p + 4q = 20,

5p – 2q = 6

see explanation

Explanation:

(a)

3x + 5y = 8 → (1)

4x - 3y = 1 → (2)

multiplying (1) by 3 and (2) by 5 and adding the result will eliminate y

9x + 15y = 24 → (3)

20x - 15y = 5 → (4)

add (3) and (4) term by term to eliminate y

29x + 0 = 29

29x = 29 ( divide both sides by 29 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (1)

9(1) + 15y = 24

9 + 15y = 24 ( subtract 9 from both sides )

15y = 15 ( divide both sides by 15 )

y = 1

solution is x = 1 , y = 1

(b)

6p + 4q = 20 → (1)

5p - 2q = 6 → (2)

multiplying (2) by 2 and adding to (1) will eliminate q

10p - 4q = 12 → (3)

add (1) and (3) term by term to eliminate q

16p + 0 = 32

16p = 32 ( divide both sides by 16 )

p = 2

substitute p = 2 into either of the 2 equations and solve for q

substituting into (1)

6(2) + 4q = 20

12 + 4q = 20 ( subtract 12 from both sides )

4q = 8 ( divide both sides by 4 )

q = 2

solution is p = 2 , q = 2

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