Whether the statement "If a system of two linear equations in two variables is dependent, then it has infinitely many solutions" is true or false.

Ava-May Nelson 2021-01-22 Answered
Whether the statement "If a system of two linear equations in two variables is dependent, then it has infinitely many solutions" is true or false.
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Expert Answer

broliY
Answered 2021-01-23 Author has 97 answers
Definition used:
1. If a system of equations has at least one solution, it is known as a consistent. If the system of equation has no solutions, it is inconsistent.
2 For a system of two linear equations in two variables, if one equation is a constant multiple of the other equation, the systems are dependent. Otherwise they are independent.
Calculation:
A consistent system is considered to be a dependent system if the equations have the same slope and the same y - intercepts.
In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair of the form (x, y) that satisfies the two equations simultaneously in the system.
Thus, a dependent system of two linear equations in two variables always represents infinitely many solutions.
Therefore, the statement is true.
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