Plant Growth and Systems of Equations

This lesson covers systems of equations, focusing on understanding and solving them through graphing. An example with two plants growing at different rates illustrates how to find the intersection point, which represents the solution. The lesson also discusses different types of solutions, including no solution, one solution, and infinitely many solutions, depending on the relationship between the equations.

What do the variables x and y represent in the context of the plant growth problem?

• x is the rate of growth, y is the initial height

• x is the initial height, y is the rate of growth

• x is the number of days, y is the height

• x is the height, y is the number of days

What is the main method discussed for solving the system of equations in this lesson?

• Substitution

• Elimination

• Matrix method

• Graphing

At what point do the graphs of the two plant growth equations intersect?

• After 20 days at 12 feet

• After 15 days at 10 feet

• After 12 days at 9 feet

• After 10 days at 8 feet

How much does plant B gain on plant A each day?

• One-half of a foot

• One-fourth of a foot

• Three-fourths of a foot

• One foot

How long does it take for the two plants to be at the same height?

• 20 days

• 10 days

• 12 days

• 15 days

What is the net gain in height difference between the two plants each day?

• One foot

• Three-fourths of a foot

• One-half of a foot

• One-fourth of a foot

What type of solution is present when two lines in a system of equations are parallel?

• No solution

• One solution

• Infinitely many solutions

• Two solutions

What type of solution occurs when two lines intersect at a single point?

• Two solutions

• Infinitely many solutions

• One solution

• No solution

What type of solution is present when two equations are essentially the same?

• Two solutions

• Infinitely many solutions

• One solution

• No solution

Which of the following is NOT a type of solution for a system of equations?

• Infinitely many solutions

• No solution

• One solution

• Two solutions