How to Solve Simultaneous Linear Equations Graphically?

How to Solve Simultaneous Equations Graphically?


A linear equation represents a straight line on a graph. If two linear equations whose straight lines intersect each other at a point, they are called simultaneous linear equations. The point of intersection is the common solution to those linear equations, and hence the solution to the pair of simultaneous equations.

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Look at the example of two linear equations x + y = 7 and x – y = 3 intersecting at a point (5, 2), so they are simultaneous linear equations and the solution is (5, 2).


Examples of simultaneous linear equations.

How to Solve Simultaneous Linear Equations Graphically?

To solve the simultaneous linear equations graphically, we find few pairs of solutions for each of the two given linear equations in two separate tables. The pair of solutions (points) of each equation are plotted in a graph and joined by a straight line. The coordinates of the point of intersection of these two straight lines are the solution of the given simultaneous equations.



Steps for solving simultaneous linear equations graphically:

Step 1: Take the first equation, and equate it for one variable x or y in terms of other variable and find some points (value of x and y) in a table.

Step 2: Take the second equation, and equate it for one variable x or y in terms of other variable and find some points (value of x and y) in a table.

Step 3: Plot the points of both equations in a graph and join the lines.

Step 4: Find the point of the intersection of two straight lines (value of x and y) which is the solution of the given simultaneous equations.


This process of solving simultaneous equations graphically will be clear by the following worked-out examples.



Worked Out Examples

 

Example 1: Solve x + y = 7 and x – y = 3 by graphical method.


Solution: Here,


x + y = 7 …………… (i)

x – y = 3 …………… (ii)


From equation (i),

        x + y = 7

or,    x = 7 – y

x

3

2

y

4

5

       

 

Points are: (3, 4) and (2, 5)


From equation (ii),

        x – y = 3

or,    x = 3 + y

x

2

4

y

-1

1

 

 

Points are: (3, 4) and (2, 5)


Now, plotting the points on the graph,


Example 1: Solution of simultaneous linear equations.


From the above graph, point of intersection is (5, 2),

  Solution: x = 5 and y = 2

Example 2: Solve 3x + y = 6 and x – 2y = 2 by graphical method.


Solution: Here,


3x + y = 6 …………… (i)

x – 2y = 2 …………… (ii)


From equation (i),

        3x + y = 6

or,    y = 6 – 3x

x

1

2

y

3

0

       

 

Points are: (1, 3) and (2, 0)


From equation (ii),

        x – 2y = 2

or,    x = 2 + 2y

x

4

6

y

1

2



Points are: (4, 1) and (6, 2)


Now, plotting the points on the graph,


Example 2: Solution of simultaneous linear equations.


From the graph, point of intersection is (2, 0),

  Solution: x = 2 and y = 0

Example 3: Solve 3x + 2y = 4 and 5x – y = 11 by graphical method.


Solution: Here,


3x + 2y = 4 …………… (i)

5x – y = 11 …………… (ii)


From equation (i),


3x + 2y = 4

or,    3x = 4 – 2y

or,    x = (4 – 2y)/3

x

0

2

y

2

-1

               

 

Points are: (0, 2) and (2, -1)


From equation (ii),

        5x – y = 11

or,    5x – 11 = y

or,    y = 5x – 11

x

2

3

y

-1

4

 

       

Points are: (2, -1) and (3, 4)


Now, plotting the points on the graph,


Example 3: Solution of simultaneous linear equations.

From the graph, point of intersection is (2, -1),

  Solution: x = 2 and y = -1

 

Do you have any questions regarding the Simultaneous Equations Graphically?

You can ask your questions or problems in the comment section below.

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