Solving Systems of Equations

This video tutorial covers solving systems of linear equations by graphing. It explains how to find solutions by identifying the intersection points of lines on a graph. The video discusses special cases such as no solution and infinite solutions, and demonstrates using the Desmos calculator for graphing. It also covers setting up equations for word problems and provides example problems to illustrate the concepts.

What is the primary method discussed in the video for solving systems of linear equations?

• Substitution

• Matrix Method

• Elimination

• Graphing

What defines a system of equations?

• A quadratic equation

• An equation with no variables

• Two or more equations with the same variables

• A single equation with two variables

What is the solution to a system of equations?

• The x-intercept of the lines

• The point where the lines intersect

• The slope of the lines

• The y-intercept of the lines

What does it mean if two lines in a system of equations are parallel?

• They intersect at multiple points

• They have no intersection point

• They intersect at one point

• They are the same line

What does it mean if two lines in a system of equations are coincident?

• They intersect at one point

• They have no intersection point

• They are the same line

• They intersect at multiple points

How can the Desmos calculator be used to solve a system of equations?

• By graphing only one equation

• By solving the equations algebraically

• By using a matrix

• By typing the equations and finding the intersection point

What is a key feature of the Desmos graph when there are infinitely many solutions?

• The lines do not intersect

• The lines are parallel

• The lines are coincident

• The lines intersect at one point

What is the first step in setting up a system of equations for a word problem?

• Solve the equations

• Identify the variables

• Graph the equations

• Find the intersection point

In the manicure and pedicure example, what do the variables M and P represent?

• M represents price and P represents money

• M represents money and P represents price

• M represents manicures and P represents pedicures

• M represents pedicures and P represents manicures

What is the total number of visits Julia made to the salon?

• 10

• 12

• 8

• 15