Solve the following system of equations:
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Solve the following system of equations:
To solve this system of equations, we'll determine if the equations are equivalent, which would imply infinite solutions.
First, observe the two equations:
Now, let's simplify Equation 2 by dividing every term by 2:
This simplifies to:
We see that simplifying the second equation results in the first equation:
Both equations are indeed the same, .
Therefore, these two equations represent the same line in a coordinate plane, meaning they have an infinite number of solutions along this line.
There are infinite solutions.
There are infinite solutions.
\( \begin{cases} x+y=8 \\ x-y=6 \end{cases} \)
When both equations represent the same line, every point on that line satisfies both equations! Think of it like having two identical roads - they overlap completely.
Simplify both equations to their simplest form. If they become identical, like both becoming , then they're the same line with infinite solutions.
No solution: parallel lines that never meet. Infinite solutions: the same line written two different ways. Always simplify first to tell the difference!
Yes! From , we get . So solutions include:
Dividing by 2 simplifies the equation without changing its meaning. and represent exactly the same line, just written differently.
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