Ava-May Nelson

2021-01-22

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.

broliY

Skilled2021-01-23Added 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$(x,\text{}y)$ 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.

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

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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