Question

Solve the following simultaneous equations by the substitution method:
2x + y = 8
3y = 3 + 4x

Answer 1

The given equations are
2x + y = 8     ....(i)
3y = 3 + 4x   ....(ii)
Now, consider equation 2x + y = 8
⇒ y = 8 - 2x     ....(iii)
Substituting the value of y in eqn. (ii), we get
3(8 - 2x) = 3 + 4x
⇒ 24 - 6x = 3 + 4x
⇒ 6x - 4x = 3 - 24
⇒ -10x = -21
⇒ x = `(21)/(10)`
Puutting the value of x in eqn. (iii), we get
y = `8 - 2(21/10)`

= `8 - (21)/(5)`

= `(40 - 21)/(5)`

= `(19)/(5)`

Thus, the solution set is `(21/10 , 19/5)`.