Question

Solve the following simultaneous equations by the substitution method:
5x + 4y - 23 = 0
x + 9 = 6y

Answer 1

The given equations are
5x + 4y - 23 = 0    ....(i)
x + 9 = 6y           ....(ii)
Now, consider equation
x + 9 = 6y
⇒ x = 6y - 9   ....(iii)
Substituting the value of x in eqn. (i), we get
5(6y - 9) + 4y - 23 = 0
⇒ 30y - 45 + 4y - 23 = 0
⇒  34y - 68 = 0
⇒  34y = 68
⇒  y = `(68)/(34)` = 2
Putting the value of y in eqn. (iii), we get
x = 6(2) - 9
= 12 - 9
= 3
Thus, the solution set is (3, 2).