Question

Solve the following simultaneous equations by the substitution method:
13 + 2y = 9x
3y = 7x

Answer 1

The given equations are
13 + 2y = 9x   ....(i)
3y = 7x     ....(ii)
Now, consider equation
3y = 7x
⇒ y = `(7)/(3)x`   ....(iii)
Substituting the value of y in eqn. (i), we get
`13 + 2(7/3 x)` = 9x

⇒ `13 + (14)/(3) x` = 13

⇒ `9x - (14)/(3) x` = 13

⇒ `(27x - 14x)/(3)` = 13
⇒ 13x = 39
⇒ x = `(39)/(13)`
= 3
Putting the value of x in eqn. (iii), we get
y = `(7)/(3) xx 3`
= 7
Thus, the solution set is (3, 7).