Given the equations:

2x-3y = 12 .............(1)

x+5y = 14.................(2)

We need to solve for x and y.

We will use the substitution method to solve.

From (2) we will rewrite x= 14-5y

Now we will substitute into (1).

==> 2x-3y = 12

==> 2(14-5y) - 3y = 12

==> 28 - 10y - 3y = 12

==> -13y = -16

==> y= 16/13

==> x= 14-5y = 14- 5*16/13 = 102/13

==> x= 102/13

**Then the answer is: x= 102/13 and y= 16/13**

We have to solve the following system of simultaneous equations

2x - 3y = 12 ...(1)

x + 5y = 14 ...(2)

From (2)

x+ 5y = 14

=> x = 14 - 5y

Substitute in (1)

=> 2(14 - 5y) - 3y = 12

=> 28 - 10y - 3y = 12

=> 13y = 16

=> y = 16/13

x = 14 - 5y = 14 - 5*(16/13)

=> x = 102/13

**The required values are x = 102/13 and y = 16/13**

The system of equations 2x-3y=12 and x+5y=14 has to be solved.

2x-3y=12 ...(1)

x+5y=14 ...(2)

Use elimination to determine the value of the variables.

(1) - 2*(2)

2x - 3y - 2x - 10y = 12 - 28

-13y = -16

y = 16/13

5*(1) + 3*(2)

10x - 15y + 3x + 15y = 60 + 42

13x = 102

x = 102/13

The solution of the given set of equations 2x-3y=12 and x+5y=14 is x = 102/13 and y = 16/13