System of equations generally refers to the system of linear equations. A system of equation is a collection of linear equations sharing same set of variables. A system of linear equations can be solved by using various methods like:

- Substitution Method
- Elimination Method
- Graphical Method
- Matrix Method

Here, we are going to study about graphical method.

For solving a system of equation by graphical method, we need to follow the following steps:**Step 1:** For the first equation, determine the value of one variable in terms of other.**Step 2:** Now, choose random numbers and substitute them** **to find the value of given variables.**Step 3: **Repeat the same process for other equation too.**Step 4: **Draw a table out of given data.**Step 5:** Mark all the points on graph for both the equations.**Step 6:** Read the intersection point of the equations from the graph. This is the required solution.

We shall understand graphical method more precisely with the help of an example.

**Example:** Solve the following system of equations graphically:

2x + 3y = 5 and x + y = 2**Solution:**

2x + 3y = 5 ...........(1)

x + y = 2 ...............(2)

Find the value of y in terms of x

From equation (1), we get

$y$ = $\frac{5-2x}{3}$

From equation (2), we get

y = 2 - x

x |
$y$ = $\frac{5-2x}{3}$ | y = 2 - x |

-2 |
3 |
4 |

-1 |
2.3 |
3 |

0 |
1.7 |
2 |

1 |
1 |
1 |

So, for equation (1), we get the points (-2, 3), (-1, 2.3), (0, 1.7) and (1, 1).

For equation (2), we get the points (-2, 4), (-1, 3), (0, 2) and (1, 1).

We obtain the following graph out of above points:

We can easily see that the two lines are intersecting at point (1, 1). Hence, the solution is:

x = 1 and y = 1.

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