Systems of Equations

Vocabulary

100

What is it called

when two or more equations are solved together?

a system of equations

200

When solving a system of equations and the final answer shows

    6 = 14

What kind of solution is this?

No solution

300

What is a system that has all the same solutions?

INFINITE solutions

400

What method is this?

solving one equation for a variable, substituting it in the other equation, and solving for the remaining variable

solving using the substitution method

500

multiplying equations so like terms have matching coefficients is the first step in what method?

elimination method

Substitution

100

Solve the system using substitution:   (___, ___)

y = 3x

2x + y = 15

2x + 3x = 15

    5x = 15

     x = 3      then sub 3 back in for x and get y.

                           (3,  9)

200

Solve the system using substitution:   (__,  __)

3y - 2x = 4

x = 3 - y

3y - 2(3 - y) = 4                    (1, 2)

3y - 6 + 2y = 4

5y - 6 = 4

5y = 10

y = 2    then sub 2 in for y and solve for x.

300

Solve using substitution:    (___,  ___)

y= -8 - 2x

3x + 2y = -5

3x + 2(-8 - 2x)= -5

3x - 16 - 4x = -5                     (-11, 14)

-x - 16 = -5

-x = 11

x = -11   then sub -11 in for x and get y.

400

Write a system:

Jax paid $26 to bowl.  It cost $5 for shoes and $7 for each game he played.  Sol had her own shoes but also paid $7 per game and spent $21.  

USE s for shoes and g for games.

5s + 7g = 26

7g = 21

500

DAILY DOUBLE - but not really.

What is the name of the clock in Beauty and the Beast?

COGSWORTH!!!   :)

Elimination

100

Solve the system.                (____, _____)

x + 3y = 47

x + y = 41

(38,  3)

200

Solve the system.         (_____,  ______)

2x + 6y = 12

2x + 2y = 4

(0, 2)

300

2x+y=2 3y= -6x+6

What is infinite solutions?

400

5x + 2y = 2

3x + 4y = 25

*There will be a decimal somewhere.

(-3,  8.5)

500

Solve the system.

3x + 8y = 19

4x - 5y = -6

(1,  2)

Solving EQUATIONS

100

Solve for m.

3(5m - 7) = 9

m = 2

200

Solve for m.

3(m + 5) = 4m

m = 15

300

Solve for P:     2 + 2P = 2(N + 1)

Options:

A)   P = N          B)  P = N - 1        C)  P = 1/2N

2 + 2P = 2(N + 1)

 2 + 2P = 2N + 2

-2                    -2

      2P = 2N                        A)   P = N

     /2       /2

400

Solve for x.

(x + 2)(x - 2) = x² + x

x² - 4 = x² + x

-x²         -x²

    -4 = x

500

Solve for X.   THERE WILL BE TWO answers

(x - 2)(x + 2) = 2x² - 8

*X could be two values

x² = 4

x = 2  and  x = -2

WORDING

100

Would you shade ABOVE or BELOW the line in the linear inequality  y > 3x + 1  ?

y >       "y is greater than...."

SHADE ABOVE

200

Write the sentence below using symbols and numbers.

Twice a boy's age (a) is 9.

2(a) = 9

300

Write an expression for the sentence below using numbers and symbols.

six more than twice a number, n.

2n + 6

400

What type of equation should be written?

Jake bought 4 cans and 3 boxes of food and paid $17.89

Standard Form

500

Find the number.

eight more than double a number is 12.6

2x + 8 = 12.6

    x = 2.3

The number is 2.3