How do you write a system of linear equations in two variables? Explain this in words and by using mathematical notation in an equation.

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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First, the definition of a "system of linear equations" is:  a set of equations (at least 2) with a minimum of 2 variables.

Usually this is done using x and y as it refers to the coordinate plane for graphing purposes, but does not have to be x and y.

A linear equation is an algebraic equation in which each term is either a constant or a product of a constant and a single variable.  Linear equations can have one or more variables.

To write the system, we will stick with using the variables x and y.  The 2 equations can be written in any form. (Slope-intercept, point-slope, standard, etc) 

I will use standard form for the equation of a line which is:  `ax + by = c.`

Therefore in order to write a system we can let a,b, and c be any constant. Using standard form:

This means I could have:  `3x -2y = 5`

                                      `5x + 4y = 2`

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