Solving Linear Equations:
In this article, we will solve a system of linear equations involving two variables, x and y. The given equations are:
1/2x - 1/3y = 5 ... (1) x = 2/3y + 10 ... (2)
Our goal is to find the values of x and y that satisfy both equations.
Step 1: Solve Equation (2) for x
We can rewrite Equation (2) as:
x = 2/3y + 10
This equation expresses x in terms of y.
Step 2: Substitute x into Equation (1)
Substituting the expression for x from Equation (2) into Equation (1), we get:
1/2(2/3y + 10) - 1/3y = 5
Step 3: Simplify and Solve for y
Simplifying the equation, we get:
2/3y + 5 - 1/3y = 5
Combine like terms:
1/3y = -5
y = -15
Step 4: Find the Value of x
Now that we have found y, we can find the value of x by substituting y into Equation (2):
x = 2/3(-15) + 10
x = -10 + 10
x = 0
Solution
The solution to the system of linear equations is x = 0 and y = -15.
In conclusion, by using substitution and simplification, we were able to solve the system of linear equations and find the values of x and y.
