Question

What is the solution of the system?

y = 14x – 1
y = –11x + 4

Answer 1

y = 14x – 1---------1

y = –11x + 4--------2

1 , 2 equtions are equal

14x - 1 = -11x + 4

add 1 to each side

14x - 1 + 1= -11x + 4 + 1

14x  = -11x + 5

add 11x to each side

14x + 11x = -11x + 11x + 5

      25x = 5

divide each side by 25

     25x / 25 = 5 / 25

        x = 1 /5

substitute x =1 /5 in the equation

y =14 (1/5) - 1

y =(14 /5) -1

y =(14 -5) /5

y =9 / 5

the solutions (x , y) = (1/5 ,9 /5)

Answer 2

y =    14x – 1------(1)
     y = –11x + 4 ------(2)

    Substitute   y = (14x –1) in equation(2) to get  x value

    Then, 14x - 1 = –11x + 4

     ⇒ 14x - 1+ 11x  = –11x + 4+ 11x

    ⇒ 25x - 1 = 4

    ⇒ 25x = 5

    ⇒ x = 5/25 =1/5

    Now substitute x = 1/5 in equation (1)

     y = 14(1/5) – 1

     y = (14 - 5)/5 = 9/5

    The values of x and y are 1/5, 9/5 respectively