Problem: The sum of two numbers is 206. If the larger number is 42 more than the smaller, what are the numbers?

In my previous post, we learned how to solve System of Linear Equation in two variables by Subtstitution Method.
https://steemit.com/math/@fabio2614/solving-sytem-of-linear-equation-in-two-variables-by-substitution-method

Today's post talks on how to solve System of Linear Equation in two variables by Elimination Method

•Abstraction

As we all know most problems that we encounter in life involve more than one variable.
In Algebra we put the relationships between variables in terms of equations so that we may be able to find values for the variables that would make the equations true statements.

These values are what we called solutions to the problem and we will learn how to determine those - though there are actually many ways in finding those solutions.

This time, we are going to find the solution to the problem by

How it is applied?
In this method , we eliminate one of the variables either by multiplying one equation or both by a non-zero numbers so that the variable we want to eliminate will have the same numerical coefficient.

Skills needed
*knowledge in addition property of equality.
It states that:

Adding two similar terms with different signs will be equal to zero - thus obtaining one equation in one unknown.

• Application to real life situation

Problem: The sum of two numbers is 206. If the larger number is 42 more than the smaller, what are the numbers?

Recall the standard form of a Linear Equation in Two Variables

Let's start!
We will use x and y to represent the two numbers - though we can use any variables to represent the unknown.

Out from our representation, we can now have the two equations.

Note:
make sure to transform each equations to standard form.

Now add the two equations

To find the value of y substitute 82 for x in either of the given equation.

We now find the following value
x= 82
y= 124
Recall that we
Let x = be the smaller number
y = be the larger number

Therefore the two numbers are 82 and 124

So problem solved!

Have a nice day steemians!