Calculator scientific calculator. What is a system of linear equations? An equation is said to be linear if all the variables appearing in the equation are first powers. In particular, variables cannot be squared or cubed, nor can they be placed under the root or in the denominator of a fraction. The only thing you can do with variables is multiply them by numbers and add those expressions together. If we have several linear equations and want to find numbers that solve all of them simultaneously, then we say we want to solve a system of linear equations. Our Elimination Calculator works on two systems of linear equations in two variables. Generally, such a system takes the form: a1x + b1y = c1 a2x + b2y = c2 where: x and y are the variables; a1, b1, c1 are the coefficients of the first equation; a2, b2, c2 are the coefficients of the second equation.