To get the second equation, use the information that says the eastbound car goes 4 mph faster than the westbound car. English: Speed of eastbound car is 4 mph faster than Speed of westbound car T T T T Equation: y 4 x The equation is y 4 x. The system of equations is 2.5x 2.5y 330 y 4 x. Step 4: Solve the system. Use substitution. 2.5x 2.5y 330 2.5x 2.5(4 x) 330 Substitute 4 x for y. 2.5x 10 2.5x 330 Distribute. 5x 10 330 Combine like terms. 5x 320 Subtract 10 from each side. x 64 Find y by substituting x 64 into y 4 x. y 4 64 68 The solution to the system is (64, 68). Step 5: Check the answer, and interpret the solution as it relates to the problem. The speed of the westbound car is 64 mph, and the speed of the eastbound car is 68 mph. Check. Distance of Distance of westbound car eastbound car T T 2.5(64) 2.5(68) 160 170 330 mi YOU TRY 5 Write an equation, and solve. Two planes leave the same airport, one headed north and the other headed south. The northbound plane goes 100 mph slower than the southbound plane. Find each of their speeds if they are 1240 miles apart after 2 hours. ANSWERS TO YOU TRY EXERCISES 1) Carson City: 55,300; Elmira: 29,200 2) width: 27 in.; length: 54 in. 3) scarf: $28; belt: $21 4) 20 mL of 5% solution; 40 mL of 17% solution 5) northbound plane: 260 mph; southbound plane: 360 mph Remember that both x and y should be positive values when working with distance, rate, and time problems. www.mhhe.com/messersmith SECTION 4.4 Applications of Systems of Two Equations 281
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