Solve the system of equations algebraically.
4x-3y=6
6x-5y=6

a. (5,7)
b. many solutions
c. no soluton
d. (6,6)

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)

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