System of Linear Equations
In this article, we will discuss a system of linear equations and how to solve it.
The Equations
We are given three linear equations:
Equation 1
1/x - 2/y + 4 = 0
Equation 2
1/y - 1/z + 1 = 0
Equation 3
2/x + 3/x = 14
Solving the System
To solve this system of linear equations, we can start by simplifying each equation.
Simplifying Equation 1
1/x - 2/y + 4 = 0
We can rewrite this equation as:
1/x = 2/y - 4
Simplifying Equation 2
1/y - 1/z + 1 = 0
We can rewrite this equation as:
1/y = 1/z - 1
Simplifying Equation 3
2/x + 3/x = 14
We can rewrite this equation as:
5/x = 14
Solving for x Now that we have simplified each equation, we can start solving for x.
From Equation 3, we know that:
5/x = 14
Multiplying both sides by x, we get:
5 = 14x
Dividing both sides by 14, we get:
x = 5/14
Solving for y Now that we have found x, we can substitute this value into Equation 1 to solve for y.
From Equation 1, we know that:
1/x = 2/y - 4
Substituting x = 5/14, we get:
1/(5/14) = 2/y - 4
Simplifying this equation, we get:
y = 1/2
Solving for z Now that we have found y, we can substitute this value into Equation 2 to solve for z.
From Equation 2, we know that:
1/y = 1/z - 1
Substituting y = 1/2, we get:
1/(1/2) = 1/z - 1
Simplifying this equation, we get:
z = 2/3
Conclusion In conclusion, we have solved the system of linear equations and found the values of x, y, and z to be:
x = 5/14 y = 1/2 z = 2/3
