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).
