Question

Solve the following system of equations by the elimination method:

0.7x + 0.3y = 1.1, 0.2x + 0.5y = –0.1

Answer 1

Given system of equations:

0.7x + 0.3y = 1.1   ...(i) 

0.2x + 0.5y = –0.1   ...(ii)

Step-wise calculation:

1. Multiply equation (i) by 5 and equation (ii) by 3 to make the coefficients of (y) equal:

5 × (0.7x + 0.3y) = 5 × 1.1 

⇒ 3.5x + 1.5y = 5.5   ...(iii) 

3 × (0.2x + 0.5y) = 3 × (–0.1) 

⇒ 0.6x + 1.5y = –0.3   ...(iv)

2. Subtract equation (iv) from equation (iii) to eliminate (y):

(3.5x – 0.6x) + (1.5y – 1.5y) = 5.5 – (–0.3) 

2.9x = 5.8 

`x = (5.8)/(2.9)`

x = 2

3. Substitute (x = 2) into equation (i):

0.7(2) + 0.3y = 1.1 

1.4 + 0.3y = 1.1 

0.3y = 1.1 – 1.4 

 0.3y = –0.3

`y = (-0.3)/(0.3)`

y = –1

Hence, the solution to the system is x = 2 and y = –1.