To fill: The blank in the statement “A system equations is
Answer to Problem 7SGR
The complete statement is “A system equations is dependent if it has infinite number of solutions”.
Explanation of Solution
Given information:
The statement “A system equations is
Consider the provided statement “A system equations is
Consider the system of linear equations with three variables.
Recall that coincident lines have infinitely many solutions.
Two lines are said to be coincident if the ratio of the coefficients of the lines are equal.
Suppose take an equation of line with three variables as,
Now, the second equation
Take a random third equation
Now, system of equations so formed is,
Since, the coefficients of all the two lines are in same ratio so the system has infinitely many solutions.
Thus, the complete statement is “A system equations is dependent if it has infinite number of solutions”.
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