Algebra I System of Equations Pg 3-1

We have found that an equation with two variables often has an infinite number of solutions. Sometimes if you have two equations they will have a solution in common:

Solutions for y = 3x – 1 Solutions for 2y + x = 12

x	y
1	5.5
2	5.0
3	4.5
4	4.0

x	y
1	2
2	5
3	8
4	11

Finding this “common solution” is what it means to solve a system of equations or to solve two equations simultaneously. Are we likely to find the common solution by listing a few solutions in a table?

1) You bought 6 lbs of apples and 3 lbs of oranges for $9. Then next day you bought 4 lbs of apples and 6 lbs of oranges for $12. Write a system of two equations for this situation (let x be the price of apples & y the price of oranges). Explain why (0.5,2) is not a solution to the system. Can you find the price per pound for oranges?

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