Choose the correct answer for the following exercise:
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Choose the correct answer for the following exercise:
To solve this system of equations, follow these steps:
Since both equations are identical after simplification, this indicates that the system represents the same line.
Therefore, the system has infinite solutions because any point that satisfies one equation will satisfy the other.
Thus, the correct answer is Infinite solutions.
Infinite solutions
Solve the following equations:
\( \begin{cases}
2x+y=9 \\
x=5
\end{cases}
\)
A system has infinite solutions when the equations represent the same line. After simplifying, if both equations are identical, every point on that line is a solution!
No solution: parallel lines that never meet (like x + y = 5 and x + y = 3). Infinite solutions: the exact same line written in different ways.
Equations can look different but represent the same line! By dividing by 2, we get , revealing they're identical.
With infinite solutions, you can pick any x-value and solve for y using the equation. For example: if x = 0, then 3y = 14, so y = 14/3.
Write "Infinite solutions" or express the relationship as . Both show that there are countless solution pairs!
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