Question

A system of equations is shown below:

Answer 1

6x + 7y = 11  . . . . (1)
5x + 2y = 13 . . . .  (2)

6x + 7y = 11  (multiply through by 2)  →   12x + 14y = 22   ($1^{a}$)

5x + 2y = 13  (multiply through by 7)  →   35x + 14y = 91   ($2^{a}$)

    by subtracting ($1^{a}$) from ($2^{a}$)

   ⇒  (35x + 14y) - (12x + 14y) = 91 - 22
     ⇒      35x - 12x + 14y - 14y = 91 - 22
                                 ⇒      23x = 69
                              ⇒ 23x ÷ 23 = 69 ÷ 23
                                          ∴  x = 3

By substituting found value of x into (2),
          ⇒     5(3)  +  2y  =  13 
          ⇒       15  +  2y = 13
          ⇒                 2y = 13 - 15
                              2y = -2
                        ∴      y = -1

Thus the solution to the system is (3 , -1)