Answer: Inconsistent and Independent
Explanation:
EQ 1: 5x + 10y + 15z = 60
EQ 2: 2x + 4y + 6z = 60
EQ 3: x + 2y + 3z = 60
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EQ 1: 5x + 10y + 15z = 60 → -2(5x + 10y + 15z = 60) → -10x - 20y - 30z = -120
EQ 2: 2x + 4y + 6z = 60 → 5(2x + 4y + 6z = 60) → 10x + 20y + 30z = 300
0 = 180
FALSE
False statement means EQ1 and EQ2 are parallel lines.
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EQ 2: 2x + 4y + 6z = 60 → -1(2x + 4y + 6z = 60) → -2x - 4y - 6z = -60
EQ 3: x + 2y + 3z = 60 → 2( x + 2y + 3z = 60) → 2x + 4y + 6z = 120
0 = 60
FALSE
False statement means EQ2 and EQ3 are parallel lines.
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EQ1 || EQ2 and EQ2 || EQ3, so EQ1 || EQ3
Since all lines are parallel to each other there will be no solution.
Inconsistent because the lines do no not cross
Independent because they do not rely on another equation
