Rearrange the equations, if necessary, so that they are in standard form. For example, if given the system of linear equations 2x + 3y = -4 and y = 12x + 2, the second equation would need to be changed to -12x + y = 2.
Determine the values of "A", "B" and "C" for each equation. If any variables are in one equation and not the other, use the value "0" for the equivalent "A," "B" or "C" constant. In the first equation, the value of "A" = 2, "B" = 3 and "C" = -4. In the second equation, the value of "A" = -12, "B" = 1 and "C" = 2.
Go to a website such as Bluebit Linear Equations Solver. In the linear equations solver, enter in the values for "A" and "B" in the box for "Coefficients' matrix A:" and the values for "C" for each in the box for "Right hand side matrix B:." Put each set of values for each equation on a new line. For example, type "2 3" on the first line, hit "Enter" and then type "-12 1" on the second line. Repeat this for any additional equations. Then enter the values for the other side of the equation in the "Right hand side matrix B:" box with the value from each equation on a new line. In the example, you would type "-4" on the first line, hit "Enter" and then type "2."
Select "Spaces" next to the "Values are delimited by:" option and choose the number of decimal places to show in the results.
Click the "Solve A*X=B" button.
Record the solution in the box under "Solution A*X=B." The first value is the "x" value and the second value is the "y" value. In the example, the solution is x = -0.263 and y = -1.158. This is the intersection of the two lines 2x + 3y = -4 and y = 12x + 2.