Find all solutions of the given system of equations and check your answer graphically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).) 6x − 5y = 3
5x − 6y = −3
(x, y) = ?

x = 3

y = 3

(3,3)

Step-by-step explanation:

Let's solve for y.

6x−5y=3

Step 1: Add -6x to both sides.

6x−5y+−6x=3+−6x

−5y=−6x+3

Step 2: Divide both sides by -5.

−5y /−5 = −6x+3 /−5

y= 6 /5 x+  −3 /5

Let's solve for y.

5x−6y=−3

Step 1: Add -5x to both sides.

5x−6y+−5x=−3+−5x

−6y=−5x−3

Step 2: Divide both sides by -6.

−6y /−6 = −5x−3 −6

y= 5 /6 x+ 1 /2

(Now let's solve for (x,y))

Solving for x =

5/6x+1/2=6/5x+−3/5

Step 1: Subtract 6/5x from both sides.

5 /6 x+ 1 /2 − 6 /5

x= 6 /5 x+ −3 /5 − 6 /5 x

−11 /30 x+ 1 /2= −3 /5

Step 2: Subtract 1/2 from both sides.

−11 /30 x+ 1 /2 − 1 /2 = −3 /5 − 1 /2 −11 /30

x= −11 /10

Step 3: Multiply both sides by 30/(-11).

(30 /−11 )*( −11 /30 x)=( 30 /−11 )*( −11 /10 )

x=3

Solving for Y:

y = 5/6(3)+1/2

y = 3

the ride was 24 km long.

Step-by-step explanation:

Let us suppose the ride was x km long.

Now, it has been given that Cyclist were 3/4 finished with their ride when they reached the 18 kilometer mark.

It means we have the equation

Multiply both sides by 4

Now, divide both sides by 3

Thus, the ride was 24 km long.