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To solve this system of equations, we need to determine the relationship between the two equations. The given equations are:
Let's examine the second equation:
Notice that if we multiply the first equation by 3, we obtain:
which simplifies to:
This is exactly the same as the second given equation. Thus, the second equation is a multiple of the first equation, indicating that they represent the same line in the coordinate plane.
When two equations represent the same line, any point on this line will satisfy both equations. Therefore, there are infinitely many solutions to this system. That is, there are infinitely many points that can satisfy both equations.
Therefore, the solution to the problem is Infinite solutions.
Infinite solutions
\( \begin{cases} x+y=8 \\ x-y=6 \end{cases} \)
Look for dependent equations - when one equation is a multiple of another. If multiplying equation 1 by some number gives you equation 2 exactly, then they're the same line with infinite solutions.
No solution: parallel lines that never meet. Infinite solutions: the same line written in different forms. Check if the ratios of coefficients match!
Multiplying reveals if equations are equivalent. When gives exactly the second equation, they represent identical lines in the coordinate plane.
With infinite solutions, you can't find one specific pair. Instead, express y in terms of x: . Any point on this line works!
Don't be fooled by appearance! Always check proportionality. Equations like and are actually the same line.
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