(PLEASE HELP!) Write and solve a system of two linear equations with the defined variables to solve the given problem.
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During the month of April, a homeowner used 770 units of electricity (x) and 90 units of natural gas (y) for a total combined utility bill of $210. In May, 830 units of electricity and 45 units of gas were used at a combined cost of $171.75. If the unit cost for each type of energy remained constant for both months, find the unit cost for each energy source.