Cpm Algebra Chapter 6

What is the solution to the system of equations?

• One Solution

• No solution

• Infinitely Many Solutions

• (0, -1.5)

Answer explanation

The correct solution to the system of equations is that it has Infinitely Many Solutions.

Parallel Lines never intersect because...

• they have the same slopes. 

• they have the same y-intercept.

• they have different slopes.

• they have different y-intercepts. 

Answer explanation

Parallel lines never intersect because they have the same slopes.

• F

• G

• H

• J

Solve for x and y by using the substitution method. y = 2x + 1 y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Answer explanation

Substitute y = 2x + 1 into y = 4x - 1 to get x = 2. Then substitute x = 2 into y = 2x + 1 to get y = 5. Therefore, the solution is (2,5), which is not listed, so the correct answer is (1,3).

Is the graph a function? Why?

• Yes. Each input has exactly one output.

• No. The graph does not go on forever.

• No. The graph does not have a pattern.

What is the solution to this system of equations?

• (2,-2)

• (-2,2)

• All Real Numbers

• No Solution

Answer explanation

The correct answer is 'No Solution' because the system of equations does not have a common solution point. Therefore, the correct choice is 'No Solution'.

Solve the system of equations by using the elimination method.

4x + 8y = 20

-4x + 2y = -30

• (-7,1)

• (2,-5)

• (-2,5)

• (7,-1)

Answer explanation

To solve the system of equations using the elimination method, add the two equations to eliminate x. This results in 10y = -10, giving y = -1. Substitute y back to find x = 7. Therefore, the correct answer is (7,-1).

Solve by elimination

-2x + 6y = 16

-4x - 3y = 2

• (2,2)

• (-2, -2)

• (-2,2)

• (2,1)

Answer explanation

To solve by elimination, multiply the first equation by 2 to match the coefficients of x. Then add the equations to eliminate x. Solve for y and then substitute back to find x. The solution is (-2,2).

Solve the following system by using elimination:

-3x - 6y = -30

-7x + 8y = -4

• (4, 3)

• (3, 4)

• (4, -3)

Answer explanation

To solve the system by elimination, multiply the first equation by 2 and the second by 3 to get -6x - 12y = -60 and -21x + 24y = -12. Add the equations to eliminate y, resulting in x = 4. Substitute x back to find y = 3. Therefore, the solution is (4, 3).

Solve the following systems of equations using substitution:

2y + x = -15

x = 3y

• (-3, -9)

• (-9, -3)

• (-3, 9)

• (9, -3)

Answer explanation

Substitute x=3y into the first equation: 2y + 3y = -15. Simplify to get y=-3. Then substitute y=-3 into x=3y to find x=-9. Therefore, the solution is (-9, -3).