I'm not altogether clear about what you mean. However, the term 'linear programming' means a category of optimisation problems in which both the objective function and the constraints are linear.
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To solve it by coordinate graphs you would take a point from the line and plug in the X and Y value into the equations and or inequalities.
It depends on the problem: you may have to use integer programming rather than linear programming.
You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
Derivative calculators are commonly used to help solve simple differential calculus equations. Generally, they are not able to solve complex calculus equations.
Gaussian elimination is used to solve systems of linear equations.