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What are the possible solutions for a pair of linear equation?
Any system of linear equations can have the following number of solutions: 0 if the system is inconsistent (one of the equations degenerates to 0=1) 1 if the system is linearly independent infinity if the system has free variables and is not inconsistent.
How do you define system linear equations?
A linear equation in n variables, x1, x2, ..., xn is an equation of the forma1x1 + a2x2 + ... + anxn = y where the ai are constants.A system of linear equations is a set of m linear equations in n unknown variables. There need not be any relationship between m and n. The system may have none, one or many solutions.
How many solutions does a system of linear equations in three variables have?
1
A system of linear equations in two variables can have solutions?
A.infinitely manyB.oneD.zero
Can a system of linear equations in two variables have infinitely solutions?
Yes.
What must be true about the lines of a system of equation that has not one solution but infinitely many solutions?
There must be fewer independent equation than there are variables. An equation in not independent if it is a linear combination of the others.
What is the solution to a linear equation?
The solution to a system on linear equations in nunknown variables are ordered n-tuples such that their values satisfy each of the equations in the system. There need not be a solution or there can be more than one solutions.
Kinds of system of linear equation in two variables?
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
Can a system of two linear equations in two variables have 3 solutions?
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
Define system of linear equation in 2 variables?
4x + 2y = 6
What does it mean for a system of linear equations to have no solutions?
It means that there is no set of values for the variables such that all the linear equations are simultaneously true.
How many solutions can a system of linear equations with two variables?
None, one or infinitely many.
