A linear system is a set of lines or linear objects that are all simultaneously true (true given the same circumstances). Together they define the solution(s) to the system.
Two methods commonly used to solve a linear system are:
Substitution and elimination is a method for solving linear system. Given two or more linear equations, this method may be used to find the solution the linear system.
Step | Equations | Description |
---|---|---|
1 | x + y = 4 x - y = 2 | Original equation |
2 | y = 4 - x x - y = 2 |
Solve the first equation for y. |
3 | y = 4 - x x - (4 - x) = 2 |
Substitute 4 - x for y in the second equation. |
4 | y = 4 - x x = 3 |
Solve the second equation for x. |
5 | y = 4 - 3 x = 3 |
Now substitute the value of x into the first equation. |
6 | y = 1 x = 3 |
Solve for y. The solution to this linear system is y = 1, x = 3. |
Example 1 |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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