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Define a consistent and independent system of equations. How many solutions does it have?
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4 stepsAnswer Question 1.
A system of equations with the same number of unknowns where its equations are consistent with each other and independent is called a consistent and independent system. This type of system has exactly one unique solution.
Answer: consistent and independent
Answer Question 2.
An ordered pair of numbers that is a solution to both equations in a system is called a solution to a system of equations.
Answer: solution
Answer Question 3 by referring to the graph.
The graph shows that the two lines intersect at the point .
Answer:
Answer Question 4.
If the lines in a system of equations coincide, they are the same line, meaning every point on the line is a solution. Therefore, the system has infinitely many solutions and is said to be consistent and dependent.
Answer: infinitely many, consistent and dependent
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