5 1 Linear Systems in 2 Variables 1 Solve the systems using any method a 2 3 11 2 4 b 3 2 10 2 5 c 2 1 3 4 2 Determine if the systems in Problem 1 are consistent or inconsistent 3 Determine if the system is dependent or independent a 2 5 4 2 10 4 A chemist needs 100 liters of 30 acid solution She has 20 and 40 acid solutions How much of each should she mix 5 Alice earns 12 hr and Bob earns 10 hr Together they worked 30 hours for 340 How many hours did each work 6 John has 55 quarters and dimes worth 7 25 How many of each coin does he have 7 Sarah drives to work at 40 mph in 45 minutes Driving back at 60 mph takes 30 minutes What s the distance 8 Amy invested at 4 and 6 interest earning 280 total interest after a year If she invested 2000 more at 4 how much did she invest in each 5 2 Distance Circles Non Linear Systems 1 Write the equations of the circles with the given center and radius a Center h k 3 56 r 3 b Center h k 5 16 r 5 c Center h k 20 3 r 3 2 The diameter of a circle has endpoints at 5 0 and 5 0 a What is the length of the diameter b Find the center of the circle c Write the equation of the circle 3 Solve the following system of equations a 2 2 36 7 b 2 2 1 2 3 c 2 2 16 2 4 4 Two cities A and B are 150 miles apart A car starts from city A and travels towards city B at an average speed of 60 mph At the same time another car starts from city B and travels towards city A at an average speed of 45 mph How long will it take for the two cars to meet 5 A circular track has a circumference of 400 meters Runner A starts at one point and runs clockwise at a constant speed of 5 m s Runner B starts at the same point but runs counterclockwise at a constant speed of 6 m s How long will it take for the two runners to meet for the first time 6 An object is launched into the air from ground level The equation gives its height meters above the ground at time in seconds the object to reach a height of 15 meters How long does it take for 5 2 20 in