 ## Solving Simultaneous Equations Graphically

While solving simultaneous equations graphically, we find few pair of solutions for each of the two given equations in two separate tables. The pair of solutions of each equation are plotted in a graph and by joining them two separate straight lines are obtained. The coordinates of the point of intersection of two straight lines are the solution of the given simultaneous equations.

Steps for solving simultaneous equations graphically:
i.         Take 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.
ii.        Take 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.
iii.       Plot the points of both equations in a graph and join the lines.
iv.       Find the point of 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.

### Workout 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 graph,
From the above graph, point of intersection is (5, 2),
x = 5
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 graph,
From the above graph, point of intersection is (2, 0),
x = 2
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 graph,

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

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