1.Solve by substitution method (show each step and give exact answers).

{ x = 5 y

2x y = 1

2.Solve by the addition method (show each step and give exact answers).

{7x 5y = 31

x + 1/4 y = 5/2

3.Write the system of two linear equations that can be used to solve each problem, then show your algebraic solving steps. State your solutions in sentence form, including any units.

a) One group of people purchased 10 hot dogs and 5 soft drinks at a cost of $35. Another group purchased 7 hot dogs and 4 soft drinks at a cost of $25.25. Find the cost of one hot dog and the cost of one soft drink.

b) A total of $8,000 was invested, part at 4% and the rest at 5% simple interest. After 1 year the total interest earned was $350. How much was invested at each rate?