Systems of Equations and Inequalities

The video tutorial covers solving mathematical problems involving parallel lines, systems of inequalities, systems of equations, and a word problem about coins. It explains how to identify parallel lines by matching slopes, solve inequalities by graphing, and solve systems of equations using substitution and elimination. The tutorial also includes a practical example of solving a word problem involving dimes and quarters.

Which equation represents a line parallel to y = -5/4x + 2?

• y = 5/4x + 2

• y = -4/5x + 2

• y = 5/4x - 1

• y = -5/4x + 1

What is the slope of a line parallel to y = -5/4x + 2?

• 4/5

• 5/4

• -5/4

• -4/5

In a system of inequalities, what does the shaded area below a line represent?

• x is greater than the line

• y is less than the line

• x is less than the line

• y is greater than the line

If two lines in a system of equations are identical, what is the nature of their solutions?

• Two solutions

• Infinite solutions

• One solution

• No solution

What is the result when you add the equations x + 3y = 7 and -x - 2y = -10?

• y = -3

• y = 3

• y = 0

• y = 7

What is the value of x in the system of equations where x + 3(-3) = 7?

• 10

• 16

• 3

• 7

How many quarters does Marcy have if she has 100 coins in total and their value is $14.05?

• 32

• 30

• 27

• 25

In the coin problem, what is the equation representing the total number of coins?

• d + q = 100

• d - q = 100

• d - q = 14.05

• d + q = 14.05

What is the equation for the total value of coins in the coin problem?

• 0.10d + 0.25q = 100

• 0.10d + 0.25q = 14.05

• 0.10d - 0.25q = 100

• 0.10d - 0.25q = 14.05

What is the first step to solve the system of equations in the coin problem?

• Multiply the first equation by 0.1

• Multiply the second equation by -0.1

• Multiply the second equation by 0.1

• Multiply the first equation by -0.1