The given system of equations can be solved using three different methods: graphical, substitution, and elimination.
Solution Using Graphical Method:
To solve the set of linear equations 2x + y = 15 and x – y = 9 graphically, plot both lines on a coordinate plane. From the plot of two lines, identify the point of intersection which is the solution for this equation (2x + y = 15) – (x – y = 9). The coordinates of that point are (6,9) therefore x=6 and y=9. This answer is also confirmed by substituting 6 for x in the second equation to get 6 – 9=-3 which does not equal 0. Thus, we have found our solution set to be {(6,9)} .
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