Question

Solve the following simultaneous equations by the substitution method:
7x - 3y = 31
9x - 5y = 41

Answer 1

The given equations are
7x - 3y = 31    ...(i)
9x - 5y = 41   ....(ii)
Now, consider equation
7x - 3y = 31
⇒ 7x = 31 + 3y
⇒ x = `(31 + 3y)/(7)`    ....(iii)
Substituting the value of x in eqn. (ii), we get
`9((31 + 3y)/(7)) - 5y` = 41

⇒ `(279 + 27y)/(7) - 5y` = 41

⇒ `(279 + 27y - 35y)/(7)` = 41
⇒ 279 - 8y = 287
⇒ -8y = 8
⇒ y = -1
Putting the value of y in eqn. (iii). we get
x = `(31 + 3(-1))/(7)`

= `(31 - 3)/(7)`

= `(28)/(7)`
= 4
Thus, the solution set is (4, -1).