Systems of Equations/Inequalities Review

Graphing Systems of Equations

100

State whether the systems of equations has 

ONE SOLUTION, NO SOLUTION or INFINITE MANY

y=-3/2x + 5

y=-2/3x +5

One Solution 

200

Does the below system of equations have 

One solution, No solution or Infinitely Many solutions?

x+y=4

3x+3y=12

INFINITE MANY

300

Write the system of equations in slope intercept form

state whether it has one, no, or infinite solutions

3x+6=y

y = 6

y=3x+6 & y=6

 One solution

400

Write the system of equations in slope intercept form

state whether the system has  one, no, or infinite solutions

2x+5=y

4x +10 = 2y

y=2x+5 

 y=2x+5

 Infinite many

500

State whether the systems of equations is 

ONE SOLUTION, NO SOLUTION or INFINITE MANY

2x + y = 4

y = -2x -2

no solution

Substitution

100

Use Substitution!!! to solve each system of equations

y = 5x + 1

4x + y = 10

(1,6)

200

Use Substitution!!! to solve each system of equations

y = -3x + 4

-6x -2y = -8

Infinitely many

300

Use Substitution!!! to solve each system of equations

5x - y = 5

-x + 3y = 13

(2,5)

400

Use Substitution!!! to solve each system of equations

y = 3x + 2

2x + 2y = 20

(2 , 8)

500

Use Substitution!!! to solve each system of equations

y = -10x -1/2

-50x - 10y = 105

(2, -41/2)

Elimination Using Addition and Subtraction

100

Use ELIMINATION to solve each system of equations.

-x + y = 7

x + y = 1

(-3, 4)

200

Use ELIMINATION to solve each system of equations.

-4x + 5y = 17

4x + 6y = -6

(-3 , 1 )

300

Use ELIMINATION to solve each system of equations.

a + 4b = -4

a + 10b = -16

( 4 , 2 )

400

2x + y = -8

x-y = 2

( -2 , -4 )

500

Jeremy and Kendrick each bought snacks for their friends at a skating rink. Jeremy bought 4 bags of popcorn and 2 plates of nachos for $18.50. Kendrick bought 7 bags of popcorn and 2 plates of nachos for $26.75

Write the systems of equations.

4x + 2y = 18.50

7x + 2y = 26.75

Elimination Using Multiplication

100

Use elimination to solve each systems of equations

x + y = 2

-3x + 4y = 15

( 1 , -3 )

200

Use elimination to solve each systems of equations

2x + 5y = 11

4x + 3y = 1

( -2 , 3 )

300

Use elimination to solve each systems of equations

12x - 3y  = -3

6x + y = 1

( 0 , 1 )

400

Mr. Santos, the curator of the children's museum, recently made two purchases of firing clay and poly clay for a visiting artist to sculpt. On Tuesday he bought 5 bogs of firing clay and 24 boxes of poly clay for $64.05. On Wednesday he bought 25 bags of firing clay and 8 boxes of poly clay for $51.45.

Create the systems of equations to represent this situation.

5x + 24y = 64.05

25x + 8y = 51.45

500

2x + 3y = 13

x + y = 7

Solve the above system of equations

( 8 , -1 )

Graphing Systems of Inequalities

100

Solve each system of inequalities by graphing.

y<6

y>x+3

Indicate 2 points that would be included in the solution

Desmos--graph

(0,5)

(-1,3)

(there are many others)

200

Solve each system of inequalities by graphing.

y < x + 10

y > 6x + 2

Indicate 2 points that would be included in the solution.

Desmos-graph

300

Solve each system of inequalities by graphing.

x + y < -1

x + y > 3

Indicate 2 points that would be included in the solution.

Desmos--graph

400

y < x + 2

y > x - 3

Solve the system of inequalities by graphing. Indicate 2 points that would be included in the solution.

Desmos-graph

500

Graph the below system of inequalities

25x + 15y > 100

x + y < 6

desmos Graph