Question

Solve the following simultaneous equations by the substitution method:
2x + 3y = 31
5x - 4 = 3y

Answer 1

The given equations are
2x + 3y = 31    ....(i)
5x - 4 = 3y     ....(ii)
Now, consider equation
2x + 3y = 31
⇒ 2x = 31 - 3y
⇒ x = `(31 - 3y)/(2)`    ....(iii)
Substituting the value of x in eqn. (ii), we get
`5((31-3y)/(2)) - 4` = 3y

⇒ `(155 - 15y)/(2) - 4` = 3y

⇒ `(155 - 15y - 8)/(2)` = 3y

⇒ 147 - 15y = 6y
⇒ 21y = 147
⇒ y = `(147)/(21) = 7`
Putting the value of y in eqn. (iii), we get
x = `(31 - 3(7))/(2)`

= `(31 - 21)/(2)`

= `(10)/(2)`
= 5
Thus, the solution set is (5, 7).