Question

Solve equations by using the substitution method.

0.2x + 0.3y =1.3 

0.4x + 0.5y = 2.3

Answer 1

Given:

0.2x + 0.3y = 1.3 

⇒ 2x + 3y = 13 …… (1) 

0.4x + 0.5y = 2.3 

⇒ 4x + 5y = 23 …… (2) 

From equation (1) 

2x = 13 – 3y 

⇒ x = \(\frac{13-3y}{2}\)

Substituting x = \(\frac{13-3y}{2}\) equation (2) we get 

\(\frac{13-3y}{2}\) + 5y = 23

⇒ 26 – 6y + 5y = 23 

⇒ -y + 26 = 23 

⇒ y = 26 — 23 = 3 

Substituting y = 3 in equaion (1) we get 

2x + 3(3) = 13 

⇒ 2x + 9 = 13 

⇒ 2x = 13 – 9 

⇒ 2x = 4 

⇒ x = 4/2 = 2 

∴ The solution is (2, 3)