Graphing Systems of Linear Equations and Savings Analysis

What is the primary focus of graphing systems of linear equations in slope-intercept form?

• To determine the area under the curve

• To identify solutions graphically

• To calculate the derivative of the equation

• To find the maximum value of the function

How many types of solutions can a system of linear equations have?

• One solution, no solutions, or infinite solutions

• Only one solution

• Only infinite solutions

• Only no solutions

What is one of the objectives of comparing different savings rates over time?

• To determine the slope of the graph

• To analyze how they impact the achievement of savings goals

• To calculate the interest rate of a loan

• To find the intersection point of two graphs

Where did you see the solution to the system of equations on the graph?

• At the intersection of the lines

• At the origin (0, 0)

• At the point where the green line crosses the x-axis

• At the point where the purple line crosses the y-axis

How can you test if a point is a solution to both equations in the system?

• Substitute the point into both equations and check if it satisfies them

• Check if the point lies on the x-axis

• Verify if the point is equidistant from the origin

• Ensure the point is at the midpoint of the graph

Tatiana starts with $8 in her piggy bank and saves $2 per week. Julian starts with $0 in his piggy bank and saves $4 per week. Write an equation to model how much money Tatiana has in her piggy bank after x weeks.

• T(x) = 8 + 2x

• T(x) = 2x

• T(x) = 8x + 2

• T(x) = 8 - 2x

Julian starts with $0 in his piggy bank and saves $4 per week.

Write an equation to model how much money Julian has in his piggy bank after x weeks.

• J(x) = 4x

• J(x) = 0 + 4x

• J(x) = 4x + 8

• J(x) = 8x

How could you identify that a system has no solutions, based on the equations in that system?

• The equations represent the same line.

• The equations have different slopes.

• The equations have the same slope but different y-intercepts.

• The equations intersect at one point.

How could you identify if a system has infinite solutions algebraically?

• The equations have different slopes.

• The equations represent the same line.

• The equations intersect at one point.

• The equations have the same slope but different y-intercepts.

Could there be a system of linear equations with exactly two solutions? Why or why not?

• Yes, if the lines intersect at two points.

• No, because two lines can only intersect at one point or overlap completely.

• Yes, if the lines are parallel.

• No, because two lines can never intersect.