Graphical method for Linear equations

Graphical method is used to find the solution of linear equations in two variables.


Example on solving equation by graphical method
x – y = 1
2x + y = 8
First, solve each equation for "y =" Or change each equation in y = mx + b form.
   x - y = 1
- x = -x
--------------
-y           - x + 1
------- = ---------
-1             -1
y = x - 1
Slope = m = 1
y intercept = -1 		  2x + y = 8
-2x = - 2x
-----------------
y = - 2x + 8
Slope = m = -2
y intercept = 8

After converting the equations in y = mx + b form, prepare a function table. Take any values of x, put that values one by one in the given equation and find the value of y. From this we get (x, y ) co-ordinates.

x
y= x-1
(x,y)
x
y =-2x+ 8
(x,y)
0
y = 0 -1
= -1
(0,-1)
0
y = -2(0) + 8
= 8
(0,8)
1
y = 1-1
= 0
(1,0)
1
y = -2(1) + 8
= -2 + 8 = 6
(1,6)
-1
y = -1 -1
= -2
(-1,-2)
-1
y = -2(-1) + 8
= 2 + 8 = 10
(-1,10)
3
y = 3 -1
= 2
(3,2)
3
y = -2(3) + 8
= - 6 + 8 = 2
(3,2)


Now, plot the points (x, y ) for a given lines and join them. The intersection point of these two lines will be the solution.




Check: Since the two lines cross at (3,2), the solution is x = 3 and y = 2.Checking these value shows that this answer is correct. Plug these values into the ORIGINAL equations and get a true result.

x - y = 1 2x + y = 8
(3) - 2 = 1 2(3)+ 2 = 8
1 = 1( check) 6 + 2 =8
8 = 8(check)


Linear equation in two variables

• Solving linear equation by graphical method.
• Substitution method.
• Solving system of equation by elimination method
• Cross multiplication method or Cramer’s rule

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