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

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 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.

Do you have a similar question?