Problem

The system of equations \( \left\{\begin{array}{l}y=-\frac{1}{2} x+6 \\ 2 x+4 y=24\end{array}\right. \) has

Answer

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Answer

The system of equations has infinitely many solutions, since the two lines are the same

Steps

Step 1 ：Substitute \( y \) from first equation into second equation: \( 2x + 4(-\frac{1}{2}x + 6) = 24 \)

Step 2 ：Simplify equation: \( 2x - 2x + 24 = 24 \)

Step 3 ：The system of equations has infinitely many solutions, since the two lines are the same

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