Question

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

Answer 1

-4

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.

Answer 2

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).

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).