Graphic solutions of two variables

Solve simultaneous linear equation

In the previous chapters we have already studied the solutions of two linear equations in this part we will study how to solve simultaneous linear equation by graphs.

Steps to follow:

• Arrange both the equations in term of any one variable.

• Prepare a point table for both the equation separately.

• Plot the point tables on graphic paper

• Find the intersection of both linear graphs

• Intersection is the solution set of both the equations.

Example:

Find the solution set graphically for the given equation.

$2x=y+5\\ x=2y+1$

Solution:

$2x=y+5\\ x=2y+1$

• Arrange both the equations in term of any one variable.

  • $y=2x-5$———(i) $y=\frac{x-1}{2}$————(ii)

• Points for $y=2x-5$

  • Put x=-2 $y=2(-2)-5$ $y=-4-5$ $y=-9$

  • Put x=-1 $y=2(-1)-5$ $y=-2-5$ $y=-7$

  • Put x=0 $y=2(0)-5$ $y=-5$

  • Put x=1 $y=2(1)-5$ $y=2-5$ $y=-3$

  • Put x=2 $y=2(2)-5$ $y=4-5$ $y=-1$

  • Points table for $y=2x-5$

  

• Apply same process for the second equation

  • Points table for $y=\frac{x-1}{2}$

  

• Plot the point tables on graphic paper and find the intersection of both linear graphs.

• We can see that $(3,1)$ is the intersection of both lines. Thus this is our Solution set of the equations.