Graphing Systems of Linear Equations: Math Task #70A

The video tutorial covers solving systems of linear equations using graphing. It begins with an introduction to linear equations and demonstrates graphing two equations to find their intersection point, which represents the solution. The tutorial verifies the solution by substituting the coordinates into the equations. It also explains the concept of parallel lines, which have no solution due to identical slopes but different y-intercepts. The video concludes with instructions for practice exercises.

What is a system of linear equations?

• Three equations with different variables

• Two equations with the same variable

• A single equation with one variable

• Two equations where you find a common solution

Where do you start graphing the equation y = 2/3x - 4?

• At y = -4

• At the origin

• At y = 4

• At x = 2/3

What is the slope of the line y = 2/3x - 4?

• 2/3

• -4

• 3/2

• -2/3

What is the intersection point of the lines y = 2/3x - 4 and y = -x + 1?

• (0, 0)

• (1, -1)

• (2, -3)

• (3, -2)

How do you verify that (3, -2) is a solution to the equation y = 2/3x - 4?

• By graphing the point

• By substituting x and y into the equation

• By finding the slope

• By checking the y-intercept

What is the result of substituting x = 3 and y = -2 into the equation y = -x + 1?

• -2 = -3 + 1

• -2 = 3 + 1

• -2 = -3 - 1

• -2 = 3 - 1

What do you call lines that never intersect?

• Skew lines

• Perpendicular lines

• Intersecting lines

• Parallel lines

Why do parallel lines never intersect?

• They are on different planes

• They have different slopes

• They have the same slope but different y-intercepts

• They have the same y-intercept

What is the solution to a system of equations with parallel lines?

• Two solutions

• No solution

• Infinite solutions

• One solution

What should you do if the lines have the same slope but different y-intercepts?

• Change the slope

• Conclude there is no solution

• Find the intersection point

• Graph more points