Solving Linear Equations using Substitution Method: 2x + 8y = 20 and y = 2
In this article, we will learn how to solve a system of linear equations using the substitution method. We will use the equations 2x + 8y = 20 and y = 2 as an example.
What is the Substitution Method?
The substitution method is a technique used to solve systems of linear equations by substituting one equation into another. This method is useful when one of the equations is easily solvable for one variable.
Given Equations
We are given two equations:
Equation 1: 2x + 8y = 20 Equation 2: y = 2
Solving Equation 2
We can solve Equation 2 for y, which gives us:
y = 2
Substituting into Equation 1
Now, we can substitute the value of y into Equation 1:
2x + 8(2) = 20
Simplifying the Equation
We can simplify the equation by multiplying 8 and 2:
2x + 16 = 20
Subtracting 16 from Both Sides
Subtracting 16 from both sides of the equation gives us:
2x = 4
Dividing Both Sides by 2
Dividing both sides of the equation by 2 gives us:
x = 2
Finding the Value of y
We already know the value of y, which is:
y = 2
Solution
Therefore, the solution to the system of linear equations is:
x = 2 y = 2
Conclusion
In this article, we have learned how to solve a system of linear equations using the substitution method. We solved the equations 2x + 8y = 20 and y = 2, and found the solution to be x = 2 and y = 2. The substitution method is a useful technique for solving systems of linear equations, and can be applied to more complex equations as well.
