9x - 5y = 5
18x - 35y = 0
Apply cross multiplication method
(x / -5 / 35 . 5 / 0 ) = (y / 5/ 0 . 9 / 18 ) =( 1 / 9 / 18 . -5 / -35 )

x / - 175= y / -90 = 1 / - 225
Comparing

x / -175= 1 / -225
--225 x = -- 175
x = -175 / - 225
x = 7 / 9

y / -90 = 1 / - 225
-225 y = -90
y = -90 / -225
y = 2 / 5

Introduction: In this question, we are given two linear equations and we need to solve them by cross multiplication method.

Cross Multiplication Method: Cross multiplication method is a technique used to solve a system of linear equations. It involves multiplying each equation by the denominator of the other equation.

Solution:

Given equations are:
9x-5y-5=0
18x-35y=0

To solve this system of equations, we can use cross multiplication method as follows:

Step 1: Multiply the first equation by the coefficient of 'y' in the second equation:
9x-5y-5=0
⇒ -5(18x-35y)= -5(0)
⇒ -90x + 175y = 0

Step 2: Multiply the second equation by the coefficient of 'y' in the first equation:
18x-35y=0
⇒ 9(9x-5y-5)=9(0)
⇒ 81x - 45y - 45 = 0

Step 3: Now we have two equations:
-90x + 175y = 0
81x - 45y - 45 = 0

Step 4: Add these equations:
-90x + 175y = 0
81x - 45y - 45 = 0
---------------------
-9x + 130y - 45 = 0

Step 5: Simplify and solve for 'y':
-9x + 130y - 45 = 0
⇒ 130y = 9x + 45
⇒ y = (9/130)x + (9/26)

Step 6: Substitute the value of 'y' in any one of the given equations and solve for 'x':
9x-5y-5=0
⇒ 9x - 5((9/130)x + (9/26)) - 5 = 0
⇒ 9x - (45/26)x - (45/26) - 5 = 0
⇒ (208/26)x = (45/26) + 5
⇒ x = 275/208

Step 7: Substitute the value of 'x' in the equation we got in step 5 and solve for 'y':
y = (9/130)x + (9/26)
⇒ y = (9/130) * (275/208) + (9/26)
⇒ y = 135/208

Therefore, the solution of the system of equations is (x, y) = (275/208, 135/208).

Conclusion: In this question, we used cross multiplication method to solve a system of linear equations. The method involves multiplying each equation by the denominator of the other equation. The final solution of the given system of equations is (x, y) = (275/208, 135/208).