Algebra 2 HS Mathematics Unit: 04 Lesson: 01
Systems of Equations KEY
Using B for the cost of a burger, F for the cost of fries, N for the cost of nachos, and S for the cost of a
soda, write equations for each statement below.
2 sodas and 3 burgers cost $18. 2S + 3B =18
5 sodas and 6 burgers cost $39. 5S + 6B = 39
2 burgers, 2 fries, and 2 sodas cost $18. 2B + 2F + 2S = 18 2 nachos, 3 burgers, 2 fries, and 4 sodas cost $38. 2N + 3B + 2F + 4S = 38
When used together, these form a system of equations, DEFINITION: which is a set of two or more equations with two or more unknowns (or variables).
The solution to a system lists the values that can be used DEFINITION: for each variable to make the equations in the system true (or, “check”).
1) 2343xyz+-=-This is a 3x3 system of equations because it uses
xz-=43 variables and has 3 equations.
--+=xyz234 ？ Which of the following would be the solution to this system? C
A) B) C) x；;4,y；;1,z；2x；9.5,y；0,z；5.5x；5,y；;3,z；1
2) This is a 2x2 system of equations because it uses 279xy-= 2 variables and has 2 equations. 1yx=-32 ？ Which ordered pair shows the solution to this system? B
A) (15, 3) B) (8, 1) C) (2, -2)
Below, circle the correct solution to each equation. How can you determine the solution? Varies
53216xyz++=3) 4) yx=-38xyz++=5 The answer is (A) The answer is (B) xy=-4185325xyz++=
A) (1, -0.2, 5.8) A) x；3,y；1
These answers are B) x；;7,y；;29B) (-2, 4, 7) called “ordered triples” C) x；7,y；;9C) (1, 1, 4)
?2012, TESCCC 07/18/12 page 1 of 1