Solve the following system of equations: -3x - y = 18 3x + y = -15
Understand the Problem
The question asks to solve a system of equations. We can use the elimination method, since the equations are structured such that we can simply add the equations to eliminate x.
Answer
No solution.
Answer for screen readers
No solution.
Steps to Solve
- Add the two equations
Adding the equations will eliminate both $x$ and $y$
$$ \begin{array}{rcrcr} -3x & - & y & = & 18 \ 3x & + & y & = & -15 \ \hline 0 & + & 0 & = & 3 \end{array} $$
- Analyze the result
The result of adding the two equations is $0 = 3$, which is never true.
- Conclusion
Since the result is a contradiction, there is no solution to this system of equations.
No solution.
More Information
The equations represent two lines that are parallel and distinct. Therefore, they never intersect, meaning there's no solution that satisfies both equations simultaneously.
Tips
A common mistake is to incorrectly perform the addition, leading to a wrong equation and subsequent incorrect solution.
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