What is meant by solutions to a set of theoretical equation with detailed explanation along with mathematical expressions.

Answer 1

Solutions to a set of theoretical equations refer to the values or sets of values that satisfy the given equations when substituted into the mathematical expressions. These solutions provide solutions for the variables in the equations such that the equations are true.

To illustrate this concept, let's consider a simple example with two equations:

Equation 1: 2x + y = 5
Equation 2: x - y = 2

The task is to find the values of x and y that satisfy both equations simultaneously. To solve this system of equations, we can use various methods like substitution, elimination, or matrix algebra. Let's solve it using the substitution method.

From Equation 2, we can express x as:
x = 2 + y

Now substitute this expression for x in Equation 1:
2(2 + y) + y = 5

Simplifying this equation:
4 + 2y + y = 5
3y + 4 = 5
3y = 5 - 4
3y = 1
y = 1/3

Now substitute the value of y back into Equation 2:
x - (1/3) = 2
x = 2 + (1/3)
x = 7/3

So, the solution to this set of theoretical equations is x = 7/3 and y = 1/3. These values satisfy both Equation 1 and Equation 2 when plugged into the respective mathematical expressions.

In summary, solutions to a set of theoretical equations are the values that make all the equations in the system true when substituted into the corresponding mathematical expressions.