Equal Values Method

• True

• False

Answer explanation

The given problem asks if we can use the 'Equal Values' method to solve this pair of equations. The correct answer is 'False'. The 'Equal Values' method applies when both equations are expressions set equal to the same variable or number, which is not the case here.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• True

• False

Answer explanation

The answer is true. The Equal Values method is a problem-solving strategy that can be used to find the solution to a system of equations. Given the two equations y=-6x+4 and y=2x-4, we can set the two y-values equal to each other and solve for x. This is essentially what the Equal Values method is.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• x = 0

• x = 1

• x = 2

Answer explanation

The system of equations given in the question is y=-6x+4 and y=2x-4. To find the value of x, we make both equations equal to each other. So, -6x+4 = 2x-4. Solving this, we get x=1, which is the correct answer.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• y = 0

• y = -1

• y = -2

Answer explanation

The question provides two equations, y=-6x+4 and y=2x-4. We're asked to substitute x=1 into these. Substituting into the first equation gives y=-6*1+4=-2, which matches the correct answer. Therefore, y=-2 is the correct choice.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• (1,-2)

• (-2,1)

Answer explanation

The solution to the system of equations is found where the two lines intersect. We know that the x-value is 1 and y-value is -2. Substituting these values into both equations, we can verify that they hold true. Therefore, the correct answer is (1,-2).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• x = 2

• x = -2

• x = 1

Answer explanation

The system of equations consists of y=4x+4 and y=x-2. Since both equations equal y, we can set them equal to each other to solve for x: 4x+4=x-2. Solving this equation, we subtract x from both sides to get 3x+4=-2, then subtract 4 from both sides to get 3x=-6. Finally, dividing both sides by 3 gives x=-2, which is the correct answer.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• y = 4

• y = 0

• y = -4

Answer explanation

The question asks us to substitute x=-2 in the equations y=4x+4 and y=x-2. Substituting x=-2 in the first equation, we get y=4(-2)+4=-8+4=-4. In the second equation, we get y=-2-2=-4. Therefore, the y-value when x=-2 in both equations is -4, which corresponds to the correct answer.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• (-4,-2)

• (-2,-4)

Answer explanation

The question asks to form an ordered pair with x-value of -2 and y-value of -4. An ordered pair always follows the pattern (x, y), so with the given values, the correct pair is (-2, -4). The option that represents this is '(-2,-4)' which matches with the correct answer.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• No solution

• Infinite solutions

Answer explanation

The question involves a system of equations. The given equations are parallel lines, which means they will never intersect. In a system of equations, a solution is where the lines intersect. As these lines do not intersect, there is no solution. Therefore, the correct answer is 'No solution'.

Tags

CCSS.8.EE.C.8B

• No solution

• Infinite solutions

Answer explanation

The given question presents a system of equations where both equations are identical. In such a scenario, every point on the line y=3x+7 is a solution because both equations will always yield the same result for the same input. Therefore, the system has an infinite number of solutions, which aligns with the correct answer option.

Tags

CCSS.8.EE.C.8B