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What kind of system has infinitely many solutions?
In order for a system to have infinitely many solutions, it must contain an equation that could be solved by any set of variables. In simple terms, a two-variable system can only be solved through two distinct equations; however, if one of these equations becomes meaningless, or could be solved by any set of variables, the other equation becomes meaningless as well because any value of y could match a given value of x. In terms of linear algebra, or any set or matrices meant to represent a system, infinitely many solutions occur due to an all 0 row. After the system is reduced to row echelon form, an all 0 row indicates that all coefficients in a given equation are equal to 0, so it does not matter what the variables are. This means that the number of equations no longer equals the number of variables and it becomes impossible to solve through cancellation and back-substitution.
Why are systems of linear inequality so important?
A system of linear inequalities give you a set of answers that could work. In day to day lives we actually use linear inequalities all the time. We are given questions and problems where we search for a number of possible solutions.
How can you find solutions for equations with two variables?
if you can, you could always search a online calculator and use that.
What it means to be a solution to a linear system algebraically?
A linear system just means it's a line. A solution is just a point that is on that line. It means that the two coordinates of the point solve the equation that makes the line. Alternatively, it could mean there are 2 (or more) lines and the point is where they intersect; meaning its coordinates solve both (or all) equations that make the lines.
Do linear equations have to be straight?
"Linear" equations are simply those where the highest power of any variable is 1 (one). There could be 2 variables in which case it is a straight line, or there might be three in which case it is a flat plane, or there might be a million in which case we don't know what it actually looks like.
