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)

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