Solving Systems of Equations

This video tutorial covers Math 8 Unit 4 Lesson 15 on writing systems of equations. It begins with an introduction to systems of equations and their solutions, including no solution, one solution, and infinite solutions. The lesson then explores real-world applications, creating and interpreting systems from scenarios like bike rides and kayak rentals. The tutorial also includes solving systems of equations with different methods and provides homework problems for practice.

What does it mean when a system of equations has no solution?

• The lines intersect at multiple points.

• The lines intersect at one point.

• The lines are parallel and never intersect.

• The lines are the same.

In a system of equations, what indicates that there is one solution?

• The lines do not intersect.

• The lines are parallel.

• The lines are identical.

• The lines intersect at one point.

How can you determine the time it takes for Lynn's dad to catch up with the family during the bike ride?

• By setting the times equal to each other.

• By setting the distances equal to each other.

• By setting the starting points equal to each other.

• By setting the speeds equal to each other.

What is the purpose of setting two cost equations equal in the kayak rental problem?

• To find the total cost for both companies.

• To calculate the hourly rate for each company.

• To determine the base fee for each company.

• To find the number of hours when costs are equal.

In the pastry problem, what does the equation 'strawberries plus apples equal 52' represent?

• The total number of fruits used.

• The total number of apples used.

• The ratio of strawberries to apples.

• The total number of strawberries used.

How do you calculate Kieran's hourly pay from the given information?

• By dividing the total earnings by the total hours worked.

• By subtracting the cousin's hours from Kieran's hours.

• By multiplying the cousin's pay by 1.3.

• By solving the system of equations for K.

What is the first step in solving the system of equations for Claire and Noah's game?

• Set up equations for goals and penalties.

• Subtract the penalties from the goals.

• Multiply the goals by the penalties.

• Add the number of goals and penalties.

In the additional practice problems, what is the solution to the equation 6x - 8 = -3x + 10?

• x = 8

• x = 2

• x = 4

• x = 6

What is the y-value when x = 2 in the equation y = 6x - 8?

• y = 2

• y = 4

• y = 6

• y = 8

How do you estimate the coordinates of the point where two lines meet?

• By finding the midpoint of the lines.

• By calculating the slope of the lines.

• By graphing the lines and finding the intersection.

• By setting the equations equal to zero.