In this article, we will discuss how to solve a two-variable system of linear equations. What is a two-variable system of linear equations? So, if there are two or more linear equations of two variables that have a relationship with each other and have one solution, it is called SPLDV. Learning SPLDV is very useful. One of the benefits is that we can determine the price of an item that we buy and can find a single value of an item, look for sales profits, to determine the size of an object.
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Method 1 of 4: Graphics Method
Step 1. Determine the coordinates of the point where the two lines intersect
The solution for SPLDV using the graphical method is done by determining the coordinates of the intersection of the two lines representing the two linear equations. Steps to solve SPLDV by graphical method:
- Draw a line that represents the two equations in the Cartesian plane.
- Find the point of intersection of the two graphs.
- The solution is (x,y).
Method 2 of 4: Substitution Method
Step 1. Change the value of a variable
The method with substitution is to replace the value of a variable in an equation from another equation. There are several steps that need to be done to solve the SPLDV with the substitution method. The steps to complete the SPLDV with the substitution method are:
- Convert one of the equations to the form y = ax + b or x = cy + d
- Substitute the value of x or y in the first step into the other equation.
- Solve the equation to get the value of x or y.
- Substitute the value of x or y obtained in the third step in one of the equations to get the value of the unknown variable.
- Do this until you get the solution for the values of x and y.
Method 3 of 4: Elimination Method
Step 1. Eliminate one of the variables
The elimination method is by eliminating one variable to determine the value of the other variable. The steps to complete the SPLDV using the elimination method are:
- Equalize one of the coefficients of the x or y variables of the two equations by multiplying the appropriate constant.
- Eliminate variables that have the same coefficient by adding or subtracting the two equations.
- Repeat both steps to get the unknown variables.
- Do this until you get the solution for the values of x and y.
Method 4 of 4: Combined Method
Step 1. Use a combination of elimination and substitution methods
This method is used most often. The combined method is a combination of elimination and substitution methods. Steps to solve SPLDV by elimination method:
- Find the value of one of the variables x or y by the elimination method.
- Use the substitution method to get the value of the second unknown variable.
- Do this until you get the solution for the values of x and y.
