Do you know about - Linear Equations - How To Predict The Nature Of Solution!
3Rd Grade Math Worksheets! Again, for I know. Ready to share new things that are useful. You and your friends.In a principles of two linear equations, there are three possibilities about the explication of the system. In this presentation, I am going to study all of three possibilities one by one.
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1. The equation have one unique solution:
The principles of two equations can have one unique solution. First of all the students need to know the meaning of one unique explication for the two linear equations. One unique explication means, if we draw both the linear equations on the graph, we get two right lines which might intersect at a point on the coordinate frame. The point of intersection is called the explication of the equations, which gives the value of both the variables.
Both the linear equations can have one explication if their slopes are different. For example; reconsider we have the following principles of linear equations:
3x + y = 2
-2x + y = -9
To find the slope we have to solve both the equations for "y" as shown below:
First equation is changed to slope and y-intercept form as
y = - 3x + 2
The coefficient of "x" which is "- 3" is the slope of line and constant term "2" is called the y-intercept.
Similarly, second equation can be changed to slope and y-intercept form as shown below:
y = 2x - 9
Slope = 2 and y-intercept = - 9 for this line.
Now, slope of first line is "- 3" and that of second line is "2".
Therefore, both the lines have separate slopes and hence have one unique solution. In other word there is one unique estimate value for variable "x" and another estimate value for "y" or in other words, if these lines are drawn on the grid, both lines will intersect at a point.
2. The equations have no solution:
There is another possibility, that the equations can't be solved and we can't find the values of variables, which is called the equations have no solution.
The process to detect this possibility is same as in case one.
Slopes and y-intercepts of both the lines are obtained and if both lines have the same slopes but separate y-intercepts, then they have no solution.
No explication means, if both lines are drawn on the grid they will be parallel to each other and never intersect with each other.
3. The linear equation got infinite many solutions:
The third possibility is that both the equations got infinite many solutions. This is the case when both the equations got same slopes and same y-intercepts. If the lines are drawn on the coordinate grid, they will overlap each other and each point is a explication for the system.
Hence, a principles of two linear equations in two variables can have above three possibilities about their solutions. The nature of the explication can be expected without solving the equation by seeing slopes and y-intercepts.
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