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Express the variables in terms of one or more parameters, which can then be manipulated to find specific solutions or describe a family of solutions.

Solve one equation for one variable and substitute into the other equation.

Graph each equation on a coordinate plane and find the intersection point(s), which represent the solution(s) to the system.

For a system with the same number of equations as unknowns, solve for each variable using determinants.

Solve the system of linear equations using matrix algebra, specifically by multiplying the inverse of the coefficient matrix with the constant matrix.

Represents the system of equations as an augmented matrix and performs row operations to arrive at a row-echelon form.

Multiply or divide equations to obtain equal coefficients for one variable, then add or subtract the equations to eliminate that variable.