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Q: Why cant a system of linear equations cannot have exactly two solutions?

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A system of linear equations can only have: no solution, one solution, or infinitely many solutions.

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In simple terms all that it means that there are more solutions than you can count!If the equations are all linear, some possibilities are given below (some are equivalent statements):there are fewer equations than variablesthe matrix of coefficients is singularthe matrix of coefficients cannot be invertedone of the equations is a linear combination of the others

Yes.

Two dependent linear equations are effectively the same equation - with their coefficients scaled up or down.

Related questions

A system of linear equations can only have: no solution, one solution, or infinitely many solutions.

Yes, a system can, in fact, have exactly two solutions.

False. There can either be zero, one, or infinite solutions to a system of two linear equations.

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A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.

No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions

They are called simultaneous equations.

Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.

Equations cannot be ordered.

As there is no system of equations shown, there are zero solutions.

It means that there is no set of values for the variables such that all the linear equations are simultaneously true.

In simple terms all that it means that there are more solutions than you can count!If the equations are all linear, some possibilities are given below (some are equivalent statements):there are fewer equations than variablesthe matrix of coefficients is singularthe matrix of coefficients cannot be invertedone of the equations is a linear combination of the others

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