Solving Systems of Equations through Graphing Techniques

The video tutorial covers solving systems of equations by graphing. It begins with an introduction to the concept and explains the different types of solutions: one solution, no solution, and infinitely many solutions. The tutorial provides multiple examples, demonstrating how to graph equations and find solutions. It also includes a real-world application example and concludes with instructions for an assignment involving task cards.

Why is it important to write equations in slope-intercept form when solving systems by graphing?

• It allows for easier addition of equations.

• It makes it easier to identify the y-intercept.

• It simplifies the process of finding the x-intercept.

• It helps in easily identifying the slope and y-intercept for graphing.

What does it mean when a system of linear equations has one solution?

• The lines are identical.

• The lines are parallel and never intersect.

• The lines intersect at exactly one point.

• The lines have the same slope and y-intercept.

In a system with no solution, what is true about the lines?

• They have the same slope but different y-intercepts.

• They are identical.

• They have different slopes and intersect at one point.

• They intersect at multiple points.

What is the solution to the system of equations y = 1/2x + 4 and y = -x + 7?

• (2, 5)

• (4, 2)

• (3, 1)

• (1, 3)

How do you convert the equation x + y = 7 into slope-intercept form?

• Divide both sides by y.

• Multiply both sides by x.

• Add x to both sides.

• Subtract x from both sides.

What is the solution to the system of equations y = 3/2x and y = 1/2x - 4?

• (0, 0)

• (-4, -6)

• (2, -2)

• (4, 6)

What is a possible second equation for a system with no solution if the first equation is y = -1/4x + 3?

• y = -1/4x + 3

• y = -1/4x + 10

• y = 1/4x + 3

• y = -1/2x + 3

Which two students' equations would have infinitely many solutions?

• Courtney and Edwin

• Ravi and Courtney

• Penny and Edwin

• Penny and Ravi

What is the equation of the line given by the points (0, 3) and (4, 2)?

• y = -1/4x + 3

• y = 1/4x + 3

• y = -1/4x - 3

• y = 1/4x - 3

If Abby bought 4 streamers and 5 balloons, what is the solution to the system x + y = 9 and y = 2x - 3?

• (6, 3)

• (3, 6)

• (5, 4)

• (4, 5)