Chapter 6 Jeopardy

Equal Values Method

100

y = −x + 8 y = x − 2

( 5, 3 )

200

k = -6p + 18 k = 3p - 9

p = 3 k = 0

300

x = 3y + 2 x = y + 2

( 2,0 )

400

y = x + 4 2x + y = 7

( 1,5 )

500

x + 2y = 4 x + 2y = 6

No Solution

Substitution Method

100

y = 2x - 3 x + y = 15

( 3,5 )

200

y=3−x y = 4x + 3

( 0,3 )

300

c = -b -11 3c + 6 = 6b

c = -8 b = -3

400

y = - x - 7 5y + 3x = -13

( -11,4 )

500

y = x - 3 2(x+y) = 18

( 6,3 )

Elimination Method

100

x − y = 11 2x + y = 19

( 10, -1 )

200

−4x − 2y = −12 4x + 8y = −24

( 6,-6)

300

3x + y = 1 x + y = 3

( -1,4 )

400

2x + 5y = 16 5x - 2y = 11

( 3,2 )

500

4x + 3y = 10 9x − 4y = 1

( 1,2 )

Solving for a Variable

100

Solve for y: 2x − y = 10

y = 2x - 10

200

Solve for y: 2y - 4x = 8

y = 2x + 4

300

Solve for m: 2(m − 3) = 4(m + 1)

m = -5

400

Solve for y: 2x−4y=12

y = (1/2)x - 3

500

Solve for x: (x + 6)(x − 3) = x^2 + 9

x = 9

How Many Solutions?/Let Statements

100

y = 6x + 5 y = 6x - 3

No Solution

200

y = 3x - 5 y = 3x - 5

Infinitely Many Solutions

300

2y = 2x + 8 y = x + 4

Infinitely Many Solutions

400

Let Statement: The Fabulous Footballers scored an incredible 55 points during last night’s game. Interestingly, the number of field goals was one more than twice the number of touchdowns. The Fabulous Footballers earned seven points for each touchdown and three points for each field goal. How many touchdowns and field goals did the Fabulous Footballers score?

Let t = the number of touchdowns Let f = the number of field goals

500

Let Statement: Barbara has a bunny that weighs 5 pounds and gains 3 pounds per year. Her cat weighs 19 pounds and gains 1 pound per year. When will the bunny and the cat weight the same?

Let x = time (years) Let y = weight (pounds)