When the system has two linear equations, you can find three possibilities of the solution by using different methods available. The first possibility is having only one and unique solution A system of two different equations may have a unique solution. At the beginning, it is good if you understand what it means to have a unique solution for the linear equation. The unique solution means that there is the linear equation at the graph and there are two straight lines that interest at just one point at the coordinated frame. Such point of intersection is known as the solution of an equation, and it gives the value of the variables. The linear equation can have one solution if the two slopes look different. The example is when there are two variables in the equation. If you want to find the slope, you should start by finding the solution of one equation. When the two lines have their own slopes, there will be a unique solution. This means that there is unique variable for x with a number as value for Y. When the lines have been drawn at the grid, the two lines can intercept at a certain point.
The equation has no solution: Sometime a linear equation may not be solved if you are not able to find the value of the variable and this is said to be an equation that does not have any solution. The process to know this possibility is one for all the linear equation. The slopes with y intercept on the two lines and they are obtained when the two lines have one slope but have two different y-intercept. This means that there is no solution. The no solution means that when these two lines have to be down at the grid, then they are going to be parallel to one another and there is no intersection of the two. When the linear equation has the infinite of the solution: The third possibility for the two equations is when there is infinite solution. This is a case when the two equations had got different slopes that have same y-intercepts. When the lines are being drawn at the coordinate grid, they will look overlapped, and each one of them will be the solution for the system. Two linear equations may have any of the above possible solutions. Nature of the solution may be predicted without having to solve an equation or finding the slopes with y-intercept. While working on the equation, they can be true or sometimes false. Sometimes they can also have a false statement. The example is 3+x=7. This equation can be false whenever another number which is not 4 is used to substitute the variable. The value of a variable where 4 is used for the variable, it is said to true. It is easy to determine if the given number or the solution to the given solution is true by substituting a number in the place of the variable and to determine falsity or truth of the results given.
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