Question

Solve the following simultaneous equations by the substitution method:
3 - (x + 5) = y + 2
2(x + y) = 10 + 2y

Answer 1

The given equations are
3 - (x + 5) = y + 2      ....(i)
2(x + y) = 10 + 2y   ....(ii)
Consider
3 - (x + 5) = y + 2
⇒ 3 - x - 5 = y + 2
⇒ -x - 2 = y + 2
⇒ x + y = -4
⇒ x = -4 - y   ....(iii)
Now, consider equation
2(x + y) = 10 + 2y
⇒ 2x + 2y = 10 + 2y
⇒ 2x = 10
⇒ x = 5
Substitutiing the value of x in eqn. (ii), we  get
5 = -4 - y
⇒ y = -4 - 5
= -9
Thus, the solution set is (5, -9).