Solving Systems of Two Equations: Strategies and Techniques

Professor Dave explains how to solve linear systems using three methods: graphing, substitution, and elimination. He discusses the conditions for unique, no, or infinite solutions and provides a real-world example involving work hours to illustrate the application of these methods.

What is the graphical solution for the system where Y = X and Y = -X + 4?

• X = 1, Y = 3

• X = 3, Y = 1

• X = 2, Y = 2

• X = 4, Y = 0

What happens when two lines in a linear system are parallel?

• No solution

• One unique solution

• Infinitely many solutions

• Depends on the equations

What does the point where two lines intersect represent in a system of linear equations?

• A possible solution

• The only solution

• No solution

• An error in the equations

In the substitution method, if you have the equations 2X + Y = 4 and X + 2Y = -1, what is the value of X?

• X = 1

• X = -1

• X = 3

• X = 2

Using substitution, what is the value of Y when X = 3 in the equations 2X + Y = 4 and X + 2Y = -1?

• Y = 1

• Y = 0

• Y = 2

• Y = -2

What is the result of adding the equations -3X + 2Y = 11 and 5X - 2Y = 5?

• Y = 35/2

• X = 3

• 2X = 16

• X = 8

What is the value of Y when X = 8 in the equations -3X + 2Y = 11 and 5X - 2Y = 5?

• Y = 35/2

• Y = 17.5

• Y = 18

• Y = 16

What method involves manipulating equations to eliminate one variable?

• Multiplication

• Elimination

• Substitution

• Graphing

How many hours did Artemis work if Penelope and Artemis together worked 70 hours and Penelope worked two hours less than twice what Artemis did?

• 30 hours

• 35 hours

• 46 hours

• 24 hours

How many hours did Penelope work given the same conditions as the previous question?

• 35 hours

• 30 hours

• 24 hours

• 46 hours