Questions: Two lines can have different slopes and therefore will have This system is said to be Two equations can be representations of the same line and therefore will have This system is said to be Two lines can have the same slope and be parallel to each other and therefore will have This system is said to be

Two lines can have different slopes and therefore will have This system is said to be
Two equations can be representations of the same line and therefore will have This system is said to be
Two lines can have the same slope and be parallel to each other and therefore will have This system is said to be

Transcript text: Two lines can have different slopes and therefore will have $\square$ This system is said to be $\square$ Two equations can be representations of the same line and therefore will have $\square$ This system is said to be $\square$ Two lines can have the same slope and be parallel to each other and therefore will have $\square$ This system is said to be $\square$

Solution

Solution Steps

For a system of two linear equations, there are three possibilities. Fill in the blanks to describe each possibility.

Two lines can have different slopes and therefore will have one point of intersection. This system is said to be consistent and independent.
Two equations can be representations of the same line and therefore will have infinitely many points of intersection. This system is said to be consistent and dependent.
Two lines can have the same slope and be parallel to each other and therefore will have no points of intersection. This system is said to be inconsistent.### Step 1: Different Slopes Two lines can have different slopes and therefore will have one point of intersection. This system is said to be consistent and independent.

Step 2: Same Line

Two equations can be representations of the same line and therefore will have infinitely many points of intersection. This system is said to be consistent and dependent.

Step 3: Parallel Lines

Two lines can have the same slope and be parallel to each other and therefore will have no points of intersection. This system is said to be inconsistent.

Final Answer

Two lines can have different slopes and therefore will have $\boxed{\text{one point of intersection}}$. This system is said to be $\boxed{\text{consistent and independent}}$.
Two equations can be representations of the same line and therefore will have $\boxed{\text{infinitely many points of intersection}}$. This system is said to be $\boxed{\text{consistent and dependent}}$.
Two lines can have the same slope and be parallel to each other and therefore will have $\boxed{\text{no points of intersection}}$. This system is said to be $\boxed{\text{inconsistent}}$.

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