How do you graph systems of linear equations in two variables?
GRAPHING is always about actually plotting the points to obtain a representative diagram.
Whether it is done manually, one individual calculation at a time, or with a graphing program, graphing always requires the calculation of a set of values from the expressions.
It doesn't matter how many different equations you have. Linear sets are, of course, easier than many other function types. In any case, set up table with columns for the 'x' variable and the expressions in terms of the 'y' variable. The range and resolution of your x-values can be adjusted to get the type of graph you need.
A wide resolution may be enough to see the relative orientation of the set. A finer resolution at the intersection point may be needed if you want to find the solution. The main difference between a single line graph and a set of linear equations is that you do want to see both lines simultaneously on the same graph, which requires some preliminary calculations to determine the best range and resolution of the x-values.
Here's an example: