Linear Equations and Their Solutions

This video tutorial covers solving systems of equations using substitution, identifying systems with one or infinite solutions, and matching graphs to equations. It also includes calculating the slope between two points. The tutorial is designed for 8th-grade students and provides step-by-step solutions to various algebraic problems.

What is the value of x when y = 6x and 4x + 6x = 7?

• 0.5

• 0.7

• 0.9

• 0.3

After finding x = 0.7, what is the value of y in the equation y = 6x?

• 2.8

• 5.0

• 3.5

• 4.2

In the system where y = 3x, what is the value of x if x = -6x + 70?

• 3

• 5

• 7

• 10

What is the value of y when x = 10 in the equation y = 3x?

• 30

• 20

• 15

• 25

Which equation, when paired with y = -1.5x + 3, results in a system with exactly one solution?

• y = -1.5x + 2

• y = -2x + 3

• y = -1.5x + 3

• y = -1.5x + 4

How can you modify the system x - 6y = 4 and 3x - 18y = 4 to have one solution?

• Change the first equation to -x - 6y = 4

• Change the second equation to 3x - 18y = 12

• Change the second equation to 3x - 18y = 5

• Change the first equation to x - 6y = 5

What change will make the system x - 6y = 4 and 3x - 18y = 4 have infinitely many solutions?

• Change the first equation to x - 6y = 5

• Change the first equation to -x - 6y = 4

• Change the second equation to 3x - 18y = 12

• Change the second equation to 3x - 18y = 5

Which graph matches an equation with a y-intercept of 3 and a slope of -2?

• Graph A

• Graph B

• Graph D

• Graph C

What is the slope of the line passing through the points (-3, 4) and (1, 7)?

• 3/4

• 1/2

• 2/3

• 1/3

Which graph corresponds to an equation with a y-intercept of -3 and a slope of 2?

• Graph C

• Graph A

• Graph B

• Graph D