To solve the system of equations:
10x - 5y = 3 (Equation 1)
6x + 30y = 81 (Equation 2)
We can use the method of substitution.
From Equation 1, we can isolate x:
10x = 5y + 3
x = (5y + 3) / 10
x = (y + 3/5) / 2 (Equation 3)
Now substitute Equation 3 into Equation 2:
6((y + 3/5) / 2) + 30y = 81
Simplify the equation:
3(y + 3/5) + 30y = 81
3y + 9/5 + 30y = 81
33y + 9/5 = 81
33y = 81 - 9/5
33y = 405/5 - 9/5
33y = 396/5
y = (396/5) / 33
y = 12/5
Substitute the value of y back into Equation 3 to find x:
x = (12/5 + 3/5) / 2
x = 15/5 / 2
x = 3/2
Therefore, the solution to the system of equations is x = 3/2 and y = 12/5.