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you call it algebra because it has an unknown number which you have to solve for
to be able to solve problems is the main purpose of studying algebra... :)
Without algebra tiles?
Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.
Language of Algebra