1Cademy - Solving $$\left\{\begin{array}{l} x + y - z = 0 \\ 2x + 4y - 2z = 6 \\ 3x + 6y - 3z = 9 \end{array}\right.$$ by Elimination

Learn Before

Solving a System of Linear Equations with Three Variables by Elimination

Example

Solving $\left\{\begin{array}{l} x + y - z = 0 \\ 2x + 4y - 2z = 6 \\ 3x + 6y - 3z = 9 \end{array}\right.$ by Elimination

To solve the system $\left\{\begin{array}{l} x + y - z = 0 \\ 2x + 4y - 2z = 6 \\ 3x + 6y - 3z = 9 \end{array}\right.$ by elimination, one can naturally eliminate the variable $x$ . Multiplying the first equation by $-2$ and adding it to the second equation directly yields the secondary equation $2y = 6$ . Multiplying the first equation by $-3$ and adding it to the third equation yields the secondary equation $3y = 9$ . Both equations logically simplify firmly to $y = 3$ . Attempting to eliminate $y$ from these two equivalent equations leads to the true mathematical statement $0 = 0$ , which solidly indicates that the original system is explicitly dependent and has infinitely many solutions. To precisely formulate the general solution, substitute $y = 3$ back into the first equation ( $x + y - z = 0$ ), which produces $x + 3 - z = 0$ . Solving strategically for $x$ in terms of $z$ safely yields $x = z - 3$ . The comprehensive solution is represented comprehensively by the continuous ordered triple $(z - 3, 3, z)$ , where $z$ firmly denotes any real number.

0

1

Updated 2026-04-25

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related