Linear Equations and Their Solutions

In this video, Mr. Boskin guides students through solving systems of equations using substitution and verification methods. He demonstrates how to find solutions for different systems, including those with one solution and infinite solutions, by altering slopes and coefficients. The video also covers graph matching and slope calculation between points, providing a comprehensive understanding of these mathematical concepts.

What is the value of x in the system of equations where y = 6x and 4x + y = 7?

• x = 0.3

• x = 0.7

• x = 0.5

• x = 1

After finding x = 0.7, what is the value of y in the system of equations where y = 6x?

• y = 4.2

• y = 1.4

• y = 3.5

• y = 2.1

In the second system of equations, what is the value of x when y = 3x and x = -2y + 70?

• x = 5

• x = 20

• x = 10

• x = 15

What is the y-value when x = 10 in the system where y = 3x?

• y = 35

• y = 30

• y = 25

• y = 20

What condition must be met for two linear equations to have exactly one solution?

• Same slope, different intercepts

• Different slopes

• Parallel lines

• Same slope and intercept

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

• Change the coefficient of x in the first equation

• Change the constant in the second equation

• Change the constant in the first equation

• Change the coefficient of y in the first equation

What change will result in a system with infinite solutions?

• Change the constant in the first equation

• Change the coefficient of y in the second equation

• Make both equations identical

• Change the coefficient of x in the second equation

Which graph corresponds to the equation y = 2x + 3?

• Graph B

• Graph A

• Graph D

• Graph C

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

• 1/2

• 3/4

• 2/3

• 5/6

Which graph represents a line with a slope of -2 and a y-intercept of 3?

• Graph A

• Graph B

• Graph D

• Graph C