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# Systems of Equations Key

By Jessica Perez,2014-11-17 00:48
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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”).

Samples:

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,z2x9.5,y0,z5.5x5,y;3,z1

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) x3,y1

These answers are B) x;7,y;29B) (-2, 4, 7) called “ordered triples” C) x7,y;9C) (1, 1, 4)

?2012, TESCCC 07/18/12 page 1 of 1

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