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Earn +20 ptsQ: When is there one solution to a system of linear equations?
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Continue Learning about Algebra
What is a system of equations that has at least one solution?
a linear equation
A system of two linear equations has exactly one solution if?
The slopes (gradients) of the two equations are different.
If a system of linear equations has exactly one solution then the two lines are what?
perpendicular
What is a unique solution in linear equations?
This is the case when there is only one set of values for each of the variables that satisfies the system of linear equations. It requires the matrix of coefficients. A to be invertible. If the system of equations is y = Ax then the unique solution is x = A-1y.
How many solutions is it possible for a system of linear equations to have?
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
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