Question

If 5y = 6x + 16 and 9x = 7y-20, what is the value of 3x - 2y?

Answer 1

The value of 3x-2y is -4. From the equation 5y=6x=16 and 9x=7y-20 the values of (x,y) is (4,8).

Step-by-step explanation:

        The given equations are,

                 5y=6x+16.......................(1)

                 9x=7y-20......................(2)

                3x-2y...............................(3)

Step:1

    Modify the equations (1) and (2) in (x+y=constant) format,

                6x-5y=-16.....................(4)

                9x-7y=-20....................(5)

Step:2

     Equation (4) is multiplied by 7     ( ∵ 7×Eqn(4))

                42x-35y=-112..............(6)

Step:3

     Equation (5) is multiplied by 5     (∵ 5×Eqn(5))

               45x-35y=-100.............(7)

Step:4

    Subtracting Equation (6) and (7)

               42x-35y=-112

              45x-35y=-100

    ( - )

     (42x-45x)+(35y-35y)=(100-112)

     (-3x)+(0)=(-12)

    x=4

Step:5

    Substitute X value in Equation (1),

             5y=6x+16...................(1)

     where, x=4,

             5y= (6×4)+16

             5y=40

            y= 8

Step: 6

      Check for solution, substitute x and y values in equation (2).

                9x=7y-20.......................(2)

               (9×4)=(7×8)-20

              36=36

Step:7

      From given, 3x-2y

      where, X=4 and y=8

              3x-2y = (3×4)-(2×8)

                        = 12-16

            3x-2y = -4

Result:

      The value for 3x-2y is -4. The values of (x,y) are (4,8).

   

Answer 2

Answer:

-4

Step-by-step explanation:

When you graph the system, the 2 lines intersect at the point (4,8). Therefore, the x is 4 and the y is 8. If you plug in 4 and 8 into 3x-2y, you get 3(4)-2(8)=12-16=-4.