To solve the given system of equations, we are required to make the coefficients of 'y' equal in both the equations. This allows us to eliminate one variable 'y' and thus, solve the system.
Let's begin solving the given system of equations:
1. We have the following equations:
(i) 10x + 5y + 1 = 15
(ii) 8x + 6y = 15
2. For equation (i), subtract 1 from both sides to normalize the equation. So, equation (i) becomes:
(iii) 10x + 5y = 14
3. Next, to make the 'y' coefficients same, multiply equation (iii) by 6 and equation (ii) by 5. This gives us:
(iv) 60x + 30y = 84
(v) 40x + 30y = 75
4. Subtracting equation (iv) from equation (v), we eliminate 'y' term and get:
20x = 9
=> x = 9/20.
So, the solution to variable x is 9/20.
5. Now, let's substitute x value into equation (i) to find the solution for 'y':
Substituting x = 9/20 into equation (i)
10*(9/20) + 5y + 1 = 15
=> 5*(9/20) + y = 14
=> 45/20 + y = 14
=> y = 14 - 45/20
=> y = 19/10.
So, the solution for variable 'y' is 19/10.
Hence, the solution to the given system of equations is x = 9/20 and y = 19/10.