Solving Systems by Graphing: Special Cases Explained

The video tutorial covers solving systems of equations by graphing. It begins with a review of the steps involved, followed by examples demonstrating how to graph equations and find their intersection points, which represent the solutions. The tutorial also discusses special cases, such as infinitely many solutions and no solution, using examples to illustrate these concepts.

What is the first step in solving a system of equations by graphing?

• Plot the x-intercept.

• Find the intersection point.

• Solve each equation for y.

• Graph the first line.

In the equation y = -x + 1, what is the slope?

• 2

• 1

• -1

• 0

What is the solution to the system of equations x + y = 1 and 2x + y = 4?

• (2, -1)

• (1, 2)

• (0, 1)

• (-1, 2)

For the equation y = -1/2x - 1, what is the y-intercept?

• 1

• 0

• 2

• -1

What is the solution to the system of equations x + 2y = -2 and 3x - 4y = -16?

• (1, -4)

• (4, -1)

• (-1, 4)

• (-4, 1)

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

• They have infinitely many solutions.

• They intersect at two points.

• They intersect at one point.

• They never intersect.

What is the term for a system of equations that results in one line?

• No solution

• One solution

• Infinitely many solutions

• Two solutions

In the equation y = -x + 4, what is the slope?

• -1

• 4

• 1

• -4

What is the solution to the system of equations x + y = 4 and x + y = -3?

• Infinitely many solutions

• (0, 0)

• No solution

• (4, -3)

If two equations are exactly the same, what type of solution do they have?

• Two solutions

• Infinitely many solutions

• One solution

• No solution