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. Box and Whiskers Plot

    Nov 18, 22 08:20 AM

    Easily learn to construct a box and whiskers plot for a set of data by using the median and the extreme values.

    Read More

  2. Binary Number System

    Nov 17, 22 10:53 AM

    This lesson will give you a deep and solid introduction to the binary number system.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes