System of Linear Equations

Vocabulary

100

the definition is: when two or more equations are considered simultaneously.

What is a system of equations?

200

an ordered pair that is the intersection of all equations in a system.

What is a solution to a system?

300

systems that have the same infinite many solutions

What is a dependent system or same equation system?

400

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

What is the substitution method?

500

multiplying equations so like terms have opposite coefficients, adding the equations, and solving the result.

What is the elimination method?

Solving Using Substitution

100

Solve the following system: y=3x-1 2x+y=9

What is (2,5)?

200

Solve the following system: 3y-2x=4 x=3-y

What is (1,2)

300

Solving the following system:x=5, y=2x-3

What is (5,7)

400

Solving the following system: 3x-6y=30 y=.5x+3

What is no solution?

500

Solving the following system: 2x-3y=7, y=3x-7

What is (2, -1)?

Solving Using Elimination

100

Solving the following system: x+3y=-9 -x+y=-7

What is (3,-4)?

200

Solving the following system: 2x+6y=-12 3x-2y=4

What is (0,-2)?

300

Solving the following system: 2x+y=2 3y=-6x+6

What is infinite many solutions?

400

Solving the following system: 5x+2y=2 3x+5y=24

What is (-2,6)?

500

Solving the following system: 0.7x+2y=1.61 2x-0.3y=0.39

What is (0.3, 0.7)?

Solving using Any Method

100

Solving the following system: 5x+y=11, x-y=1

What is (2,1)?

200

Solving the following system: x+y=-1, x-y=3

What is (1,-2)?

300

Solving the following system: y=-3x, x+y=2

What is (-1,3)?

400

Solving the following system: 2x-4y=-4 3x-y=4

What is (2,2)?

500

Solving the following system:y = 6x-6, -3x-3y=-24

What is (2,6)

Application Problems

100

The sum of two numbers is 12, and their difference is 6. What are the two numbers?

What is (3,9)?

200

Twice a boy's age is 9 more than his brother's? The average of their ages is 12. How old are they?

What is (11,13)?

300

A girl has $6 in 36 coins (all quarters and nickels). How many of each does she have?

What is 21 quarters, 15 nickels?

400

My mom's cell phone costs $10 per month plus $0.10 per minute. My aunt's phone costs $3 per month plus $0.15 per minute. For what amount of talking time will the cost of these plans be the same?

What is 140 minutes?

500

How many liters of a 60% salt mixture must be added to 2 liters of a 30% salt mixture to yield a 48% mixture?

What is 3 liters?