Introduction:
Cross multiplication method is one of the efficient ways to solve a system of linear equations. It is also known as the elimination method, where we multiply one equation by a constant and subtract it from the other equation to eliminate one variable.

Steps to Solve:
To solve the given system of equations using the cross multiplication method, follow the steps below:

Step 1: Rearrange the equations:
Rearrange the given equations in the standard form of ax+by=c.

Given equations are:
3x-5y=20
7x+2y=17

We can rewrite the equations as:
3x-5y=20 … (1)
7x+2y=17 … (2)

Step 2: Multiply the equations:
Choose one variable from the equations and multiply it by a constant such that its coefficient becomes equal in both equations. In this case, we can choose y and multiply equation (2) by 5 and equation (1) by 2.

Multiplying equation (2) by 5, we get:
35x+10y=85 … (3)

Multiplying equation (1) by 2, we get:
6x-10y=40 … (4)

Step 3: Eliminate the variable:
Now, subtract equation (4) from equation (3) to eliminate y.

35x+10y=85
- (6x-10y=40)
-----------------
29x=45

Simplifying the above equation, we get:
x=45/29

Step 4: Find the value of other variable:
Substitute the value of x in any of the given equations to find the value of y.

Using equation (1),
3(45/29) - 5y = 20
Simplifying the above equation, we get:
y=-11/29

Step 5: Check the Solution:
Verify the values of x and y by substituting them in both equations and checking if they satisfy the equations.

Using equation (1),
3(45/29) - 5(-11/29) = 20
Simplifying the above equation, we get:
20=20

Similarly, using equation (2), we get:
7(45/29) + 2(-11/29) = 17
Simplifying the above equation, we get:
17=17

Conclusion:
Therefore, the solution of the given system of equations using the cross multiplication method is x=45/29 and y=-11/29.