Algebra 1 - Unit 5 Quiz

Select the correct equation that is parallel to y = 5x - 8

• y = 5x - 8

• y = 5x - 10

• y = 1/5x + 3

• y = -1/5x - 8

Answer explanation

The equation y = 5x - 10 is parallel to y = 5x - 8 because they have the same slope (5). Parallel lines have identical slopes, while the other options either have different slopes or are the same line.

Classify the following system of equations:

• Parallel

• Coincident

• Perpendicular

• IBNP

Answer explanation

The system of equations is classified as perpendicular because the slopes of the lines represented by the equations are negative reciprocals of each other, indicating they intersect at a right angle.

Tags

CCSS.8.EE.C.8B

Classify the following system of equations:

• Parallel

• Coincident

• Perpendicular

• IBNP

Answer explanation

The system of equations is classified as parallel because the lines represented by the equations have the same slope but different y-intercepts, indicating they will never intersect.

Tags

CCSS.8.EE.C.8B

What is the solution to the system of equations graphed?

• (-1, 2)

• (-2, 1)

• (1, -2)

• (-2, -1)

Answer explanation

The solution to the system of equations is the point where the lines intersect. The point (-2, 1) is where both equations are satisfied, making it the correct answer.

Tags

CCSS.8.EE.C.8B

What is the solution to the system of equations graphed?

• (3, 1)
• (1, 3)

• (0, 4)

• (2, 0)

Answer explanation

The solution to the system of equations is the point where the lines intersect. The correct ordered pair is (3, 1), which represents the coordinates of this intersection on the graph.

Tags

CCSS.8.EE.C.8B

When does a system of equations have NO SOLUTIONS?

• Parallel Lines

• Perpendicular Lines

• IBNP Lines

• Coincident Lines

Answer explanation

A system of equations has no solutions when the lines are parallel. This means they never intersect, indicating that there is no point that satisfies both equations. Perpendicular and coincident lines do have solutions.

Tags

CCSS.8.EE.C.8A

Coincident lines have ____________ number of solutions

• One

• None

• Infinite

Answer explanation

Coincident lines are lines that lie on top of each other, meaning they have all their points in common. Therefore, they have an infinite number of solutions, as any point on the line is a solution.

Tags

CCSS.8.EE.C.8A

What is the solution to the system of equations graphed?

• One Solution

• No Solution

• Infinitely Many Solutions

Answer explanation

The system of equations has no solution because the lines are parallel and do not intersect. This means there are no points that satisfy both equations simultaneously.

Tags

CCSS.8.EE.C.8B

Solve by substitution:

y = 7x

y = 4x + 3

• (1, 7)

• (7, 1)

• (-1, -7)

• (-7, 1)

Answer explanation

To solve by substitution, set 7x = 4x + 3. This simplifies to 3x = 3, giving x = 1. Substituting x back into y = 7x gives y = 7. Thus, the solution is (1, 7), which is the correct answer.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve by substitution:

2x + 10y = -32

x = -9y

• (-4, 36)

• (36, -4)

• (-36, 4)

• (4, -36)

Answer explanation

Substituting x = -9y into 2x + 10y = -32 gives 2(-9y) + 10y = -32. Simplifying leads to -18y + 10y = -32, or -8y = -32, resulting in y = 4. Substituting y back gives x = -36. Thus, the solution is (-36, 4).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6