Option d. (6,6)
Step-by-step explanation:
(1) 4x-3y=6
(2) 6x-5y=6
Using the equal values method. Let's isolate "x" from each equation:
(1) 4x-3y=6
Adding 3y to both sides of the equation:
4x-3y+3y=6+3y
4x=6+3y
Dividing both sides of the equation by 4:
Isolating "x" from the second equation:
(2) 6x-5y=6
Adding 5y to both sides of the equation:
6x-5y+5y=6+5y
6x=6+5y
Dividing both sides of the equation by 6:
Equaling y:
y=y
Solving for "y": Cross multiplication:
6(6+3y)=4(6+5y)
Applying the distributive property:
6(6)+6(3y)=4(6)+4(5y)
36+18y=24+20y
Subtracting from both sides 18y and 24:
36+18y-18y-24=24+20y-18y-24
12=2y
Dividing both sides by 2:
12/2=2y/2
6=y
y=6
Replacing y by 6 in the any of the equations where we isolated "x":
The solution is (x,y)=(6,6)