**Solve a system of equations by graphing :**

This is one of the methods used to solve a pair of linear equations.

In this method, we have to draw the graph for each lines separately.The point in which the given lines are intersecting is the solution of the given lines.

Let us see some example problems to understand the concept.

**Example 1 :**

Solve this system of equations by graphing.

y = x – 3

y = 3

**Solution :**

**To solve the system of equations, first we have to draw the graph of the given equations one by one.**

Graph of y = x – 3

To find x -intercept, we have to put y = 0

0 = x - 3

x = 3

To find y-intercept, we have to put x = 0

y = 0 - 3

y = -3

So far we got two points for the first line (3, 0) and (0, -3). Graph of the first line y = x - 3

Graph of the second line y = 3

From the above graph we come to know that the above two lines are intersecting at the point (6, 3).

Hence (6, 3) is the solution.

**Example 2 :**

Solve this system of equations by graphing.

y = -2 x + 2

y = -5 x – 1

**Solution :**

Graph of y = -2 x + 2

x -intercept: put y = 0 -2 x + 2 = 0 -2 x = -2 x = 1 |
y-intercept put x = 0 y = -2(0) + 2 y = 0 + 2 y = 2 |

So far we got two points for the first line (1, 0) and (0,2)

Graph of y = -5 x -1

x -intercept: put y = 0 -5 x - 1 = 0 -5 x = 1 x = -1/5 = -0.2 |
y-intercept put x = 0 y = -5(0) - 1 y = 0 - 1 y = -1 |

So far we got two points for the first line (-0.2, 0) and (0,-1)

From the above graph we come to know that the above two lines are intersecting at the point (-1, 4).

Hence (-1, 4) is the solution.

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