3x-5y-4=0

=> 3x-5y=4.......(1)

9x=2y+7

=> 9x-2y=7......(2)


Multiplying eq (1) by 3 and we get,
9x -15y=12
subtracting 9x - 2y= 7
- + -
______________
-13y=5
=> y = -5/13
substituting the value of y in eq (1)

3x-5(-5/13)=4

=> 3x + 25/13 = 4

=> 3x = 27/13

=> x = 9/13


Hence the values of x and y are 9/13 and -5/13 respectively

**Pair of Linear Equations**

In mathematics, a pair of linear equations in two variables is a system of two equations that contain two variables. The general form of a linear equation in two variables can be written as follows:

ax + by = c

Where a, b, and c are constants and x and y are variables.

**Elimination Method**

The elimination method is a technique used to solve a system of linear equations by eliminating one variable. The goal is to add or subtract the equations in such a way that one variable is eliminated, leaving a new equation with only one variable. This new equation can then be solved to find the value of the remaining variable.

The elimination method involves the following steps:

1. Rearrange the equations so that the variables line up vertically.
2. Multiply one or both equations by appropriate constants to make the coefficients of one of the variables equal in magnitude but opposite in sign.
3. Add or subtract the equations to eliminate one variable.
4. Solve the resulting equation for the remaining variable.
5. Substitute this value back into one of the original equations to find the value of the other variable.
6. Check the solution by substituting the values of x and y back into both original equations to ensure they are satisfied.

**Solving the Equations**

Let's solve the given pair of linear equations using the elimination method:

Equation 1: 3x - 5y = 4
Equation 2: 9x - 2y = 7

To eliminate the variable y, we can multiply Equation 1 by 2 and Equation 2 by 5:

2(3x - 5y) = 2(4) (Equation 1)
5(9x - 2y) = 5(7) (Equation 2)

Simplifying these equations, we get:

6x - 10y = 8 (Equation 3)
45x - 10y = 35 (Equation 4)

Now, subtract Equation 3 from Equation 4 to eliminate y:

(45x - 10y) - (6x - 10y) = 35 - 8
45x - 10y - 6x + 10y = 27
39x = 27

Divide both sides of the equation by 39:

x = 27/39
x = 9/13

Substitute this value back into Equation 1 to find the value of y:

3(9/13) - 5y = 4
27/13 - 5y = 4

Multiply both sides of the equation by 13 to eliminate the fraction:

27 - 65y = 52

Subtract 27 from both sides:

-65y = 52 - 27
-65y = 25

Divide both sides of the equation by -65:

y = 25/-65
y = -5/13

Therefore, the solution to the given pair of linear equations is x = 9/13 and y = -5/13.

**Checking the Solution**

Let's substitute the values of x and y back into both original equations to verify the solution:

Equation 1: 3x - 5y = 4
3(9/13) - 5(-5/13) = 4