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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