Elimination Method for Solving Equations
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. Here's how we can solve the given equations:

Equations:
7x - 2y = 5
15x - 26y = -3

Step 1: Multiply Equations
To eliminate one variable, we need to make the coefficients of either x or y the same in both equations. Let's multiply the first equation by 13 and the second equation by 7 to make the coefficients of y the same:
91x - 26y = 65
105x - 182y = -21

Step 2: Subtract Equations
Now, subtract the modified first equation from the modified second equation to eliminate y:
105x - 182y - (91x - 26y) = -21 - 65
105x - 182y - 91x + 26y = -86
14x - 208y = -86

Step 3: Solve for x
Now, we have one equation with only x. Solve for x:
14x - 208y = -86
14x = 208y - 86
x = (208y - 86) / 14
x = 14y - 6.14

Step 4: Substitute x into one of the original equations
Now, substitute the value of x into the first original equation to solve for y:
7(14y - 6) - 2y = 5
98y - 42 - 2y = 5
96y - 42 = 5
96y = 47
y = 47/96

Step 5: Find the value of x
Now substitute the value of y back into the equation x = 14y - 6:
x = 14(47/96) - 6
x = 47/12
Therefore, the solution to the system of equations is x = 47/12 and y = 47/96.