# Solve a system of linear equations by using a table

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)

## Recent Articles

1. ### How To Find The Factors Of 20: A Simple Way

Sep 17, 23 09:46 AM

There are many ways to find the factors of 20. A simple way is to...

2. ### The SAT Math Test: How To Be Prepared To Face It And Survive

Jun 09, 23 12:04 PM

The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.