Advanced Solving Systems

Explain the concept of intersection point in the context of the graphical method for solving a system of equations.

• The intersection point represents the solution to the system of equations.

• The intersection point is the average of the two equations' slopes.

• The intersection point is the y-intercept of the first equation.

• The intersection point is the maximum value of the system of equations.

How can you determine the number of solutions to a system of equations using the graphical method?

• By finding the area under the curve

• By looking at the y-intercept

• By calculating the slope of the lines

• By counting the number of intersection points on the graph.

Compare and contrast the substitution and elimination methods for solving a system of equations.

• Substitution method always leads to the correct solution, while elimination method is unreliable

• Substitution method involves adding the equations together, while elimination method involves multiplying the equations

• Both methods involve manipulating the equations to solve for one variable and then substituting or eliminating that variable to solve for the other variables.

• Substitution method only works for linear equations, while elimination method only works for quadratic equations

Solve the system of equations: 

• ( -2, 3, -3)

• None of these

• ( -2, -3, 3)

• ( -3, 3, -2)

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

3x + y = 1
y = 4x + 1

• (0, -1)

• No Solution

• (0, 8)

• (0, 1)

y = -2x + 18
y = 8

• (5, 8)

• (-5, 8)

• (2, 8)

• (-2, 8)

7x + y = -20
y = 3x + 10

• (-3, 1)

• (-1, -3)

• (-3,-7)

• (-1,7)