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

one that is bigger than 3 1/2