One month, a homeowner used 150 units of gas and 520 units of electric for a total cost of $84.20. The next month, 210 units of gas and 405 units of electric were used for a total cost of $82.35. Find the cost per unit of gas and electric.

Let g represent the cost of gas and e represent the cost of electricity.

150g + 520e = 84.20  ⇒  7(150g + 520e = 84.20)   ⇒  1050g + 3640e = 576.80

210g + 405e = 82.35  ⇒ -5(210g + 405e = 82.35)  ⇒  -1050g - 2025e = -411.75

                                                                                                        1615e = 165.05

                                                                                                                e = 0.10

150g + 520(0.10) = 84.20

150g + 52 = 84.20

140g = 32.20

     g = 0.23

gas = $0.23, electricity = $0.10