# 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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