Learn to solve a system of linear equations by using a table with the two examples below.

**Example #1**

Solve the system below by making a table.

y = x - 2

y = -2x + 7

To make this table, you can choose 0, 1, 2, 3, and 4 as values for x and see if there is a common y-value. If you could not find a common y-value, then you can perhaps choose more values for x that are either negative numbers or positive numbers.

x | 0 | 1 | 2 | 3 | 4 |

y = x - 2 | -2 | -1 | 0 | 1 |
2 |

y = -2x + 7 | 7 | 5 | 3 | 1 |
-1 |

Take a close look at the table and you will see that when x = 3, the common y-value is 1.

Therefore, the solution to the system is (3, 1)

**Example #2**

Solve the system below by making a table.

x + y = 2

2x + 4y = 12

The system above is equivalent to

y = 2 - x

y = 3 - (1/2)x

To make this table, you can again choose 0, 1, 2, 3, and 4 as values for x and see if there is a common y-value. If you could not find a common y-value, then you can perhaps choose more values for x that are either negative numbers or positive numbers.

x | 0 | 1 | 2 | 3 | 4 |

y = 2 - x | 2 | 1 | 0 | -1 | -2 |

y = 3 - (1/2)x | 3 | 10/4 | 2 | 6/4 | 1 |

Looking closely at the table, we cannot see a common y-value. Let us then make another table and choose some values for x that are negative numbers and see what will happen.

x | -1 | -2 | -3 | -4 | -5 |

y = 2 - x | 3 | 4 |
5 | 6 | 7 |

y = 3 - (1/2)x | 14/4 | 4 |
18/4 | 5 | 22/4 |

Take a close look at the table and you will see that this time when x = -2, the common y-value is 4.

Therefore, the solution to the system is (-2, 4)