2.1-3 Quiz

Question 1

System of Equations

Answer 1

Two or more linear equations

Question 2

System of Equations Methods to Solve

Answer 2

1) Graph - y=mx+b
2) Substitution - one variable is isolated
3) Elimination - ax+by=c

Question 3

One Solution

Answer 3

Crosses at one point - (x, y)

Question 4

No Solution

Answer 4

Parallel lines - # not equal #

Question 5

Infinitely Many Solutions

Answer 5

Same line - # = #

Question 6

Algebraic Ways to Solve Systems of Equations

Answer 6

Substitution and elimination

Question 7

Steps to Solve by Substitution

Answer 7

1) Solve one equation for x or y - isolate a variable
2) Substitute the resulting equation from step 1 into the other equation for that variable
3) Solve for the remaining variable
4) Substitute your answer from step 3 into either original equation to find the other variable

Question 8

Steps to Solve by Elimination

Answer 8

1) Line up the equations
2) Multiply one or both equations by a number to result in a variable with the same coefficient
3) Add or subtract the equations to eliminate the variable
4) Solve for the remaining variable
5) Substitute your answer from step 4 into either original equation to find the other variable

Question 9

Steps to Solve Systems of Equations Applications

Answer 9

1) Define your variable - what you are solving for
2) Set up two equations using the information given
3) Solve the system using your method of choice

Question 10

Steps to Solve Systems with Three Variables

Answer 10

1) Choose two equations in which you can easily eliminate a variable - equation A
2) Eliminate the same variable from a combination of the equation you didn’t use and one of the ones you did - equation B
3) Put equation A and B together and solve that system to find two of your variables
4) Substitute your answers from step 3 into either original equation to find the remaining variable

Question 11

Systems with Three Variables Solution

Answer 11

Ordered triple - (x, y, z)