There are various methods to solve linear equations like elimination method, substitution method etc. There is another method by which we can solve linear equations, called graphical method. In this method we need to draw graphs of given equations and the point of contact or the point where both the equation intersect each other becomes the solution of the linear equation. Now understand the steps to solve linear equation graphically.
Steps to Solve Linear Equation Graphically
Step1: Take first linear equation and put x = 0, you will get value of y. lets say y = a, it will give you first point (0,a).
Step2: Now put y = 0, it will give you value of x, lets say x = b, it will give you second point (b,0)
Step3: Plot both points and draw a line between them and extend this line beyond these points, This will be graph of first linear equation.
Step4: Repeat step 1,2,3 for second linear equation, you will get graph of second linear equation.
Step5: Find out the point where these lines intersect each other, lets say point is (u,v)
the solution will be x = u, y = v
Note: In case, both lines does not intersect extend both the lines to find intersecting point and once you get intersecting point, it will be required solution. Only parallel line does not intersect each other.
Algebra is widely used in day to day activities watch out for my forthcoming posts on Online Algebra Calculator and algebra 1. I am sure they will be helpful.
Example to Solve Linear Equation Graphically
The following example will make more clear to you how to solve linear equation graphically.
Question: Solve: x + y = 1 and 2x + y = -2
Solution: x + y = 1
put x = 0, w get y = 1, so first point will be (0,1)
put y = 0, we get, x = 1, so second point will be (1,0)
2x + y = -2
put x = 0, we get, y = -2, so first point will be (0, -2)
put y = 0, we get, x = -1, so second point will be (-1, 0)
Now drawing both the lines on graph we get,
We can see that these lines cut each other at point (-3, 4)
Hence Solution will be x = -3 and y = 4.
Steps to Solve Linear Equation Graphically
Step1: Take first linear equation and put x = 0, you will get value of y. lets say y = a, it will give you first point (0,a).
Step2: Now put y = 0, it will give you value of x, lets say x = b, it will give you second point (b,0)
Step3: Plot both points and draw a line between them and extend this line beyond these points, This will be graph of first linear equation.
Step4: Repeat step 1,2,3 for second linear equation, you will get graph of second linear equation.
Step5: Find out the point where these lines intersect each other, lets say point is (u,v)
the solution will be x = u, y = v
Note: In case, both lines does not intersect extend both the lines to find intersecting point and once you get intersecting point, it will be required solution. Only parallel line does not intersect each other.
Algebra is widely used in day to day activities watch out for my forthcoming posts on Online Algebra Calculator and algebra 1. I am sure they will be helpful.
Example to Solve Linear Equation Graphically
The following example will make more clear to you how to solve linear equation graphically.
Question: Solve: x + y = 1 and 2x + y = -2
Solution: x + y = 1
put x = 0, w get y = 1, so first point will be (0,1)
put y = 0, we get, x = 1, so second point will be (1,0)
2x + y = -2
put x = 0, we get, y = -2, so first point will be (0, -2)
put y = 0, we get, x = -1, so second point will be (-1, 0)
Now drawing both the lines on graph we get,
We can see that these lines cut each other at point (-3, 4)
Hence Solution will be x = -3 and y = 4.
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