Elimination Practice

Solve by elimination:
4x+9y=28
-4x-y=-28

• (-7,0)

• (6,0)

• (-6,0)

• (7,0)

Answer explanation

The given question is a system of linear equations. By adding the two equations, we eliminate 'x'. The resulting equation is 8y=0, which gives y=0. Substituting y=0 in the first equation, we get 4x=28, which gives x=7. So, the solution is (7,0).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

4x +  8y = 20
-4x + 2y = -30
Which variable will be eliminated?

• The  x

• The  y

• The  z

• The unknown

Answer explanation

In the given question, we are asked which variable will be eliminated. By adding the two equations, we can see that the 'x' terms cancel each other out, leaving only 'y'. Therefore, the variable that will be eliminated is 'x', which is the correct answer.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What would be the first step in finding the solution with elimination?

4x + 3y = 1

x - 3y = -11

• cross out the 3y and -3y

• cross out the 4x and x

• change all the signs of the second equation

• add 1 and -11

Answer explanation

The first step in solving the given equations using the elimination method is to eliminate one of the variables. In this case, the coefficients of 'y' in both equations are the same but with opposite signs, hence, we can eliminate 'y' by adding the two equations. Therefore, the correct choice is to 'cross out the 3y and -3y'.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Identify the solution to this system of equations.

• (4, -1)

• (-1, 4)

• (-4, 1)

• (-4, -1)

Answer explanation

To solve the given system of equations, we need to find the values of x and y that satisfy both equations simultaneously. By solving the equations, we find that the correct solution is (4, -1), which corresponds to the first option. This means that x = 4 and y = -1 satisfy both equations in the system.

Tags

CCSS.8.EE.C.8B

Which variable will be eliminated?

• x

• y

Answer explanation

The question asks which variable will be eliminated. The options provided are 'x' and 'y'. The correct choice is 'x', as indicated by the given answer. Therefore, the variable that will be eliminated is 'x'.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What is the slope and the y intercept of the following?
y = 3x - 9

• Slope = 3
  y-int = 9

• slope = 3
  y-int = -9

• slope = -9
  y-int = 3

• slope = 9
  y-int = -3

Answer explanation

The question asks for the slope and y-intercept of the equation y = 3x - 9. The equation is in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Comparing the given equation with the slope-intercept form, we can see that the slope (m) is 3 and the y-intercept (b) is -9. Therefore, the correct choice is 'slope = 3, y-int = -9'.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

A system of two intersecting lines will have how many solutions?

• One Solution

• Two Solutions

• No Solution

• Infinite Solutions

Answer explanation

In a system of two intersecting lines, there is only one point where the lines meet, which represents the unique solution. Therefore, the correct choice is 'One Solution'.

Tags

CCSS.8.EE.C.8B

A system of two parallel lines will have how many solutions?

• One Solution

• Two Solutions

• No Solution

• Infinite Solutions

Answer explanation

In a system of two parallel lines, there will be no solution. This is because parallel lines never intersect, and a solution would require a point of intersection between the two lines. Since there is no such point, there is no solution to the system.

Tags

CCSS.8.EE.C.8B

A system of two identical (overlapping) lines will have how many solutions?

• One Solution

• Two Solutions

• No Solution

• Infinite Solutions

Answer explanation

In a system of two identical lines, the lines completely overlap each other. This means that every point on one line is also a point on the other line. Therefore, there are infinite solutions, as there are infinite points where the lines intersect.

Tags

CCSS.8.EE.C.8A

The solution to a system of equations is any ordered pair that makes both equations true. 

• TRUE

• FALSE

Answer explanation

The statement in the question is indeed true. A solution to a system of equations is an ordered pair that satisfies both equations simultaneously. This means that when the values of the ordered pair are substituted into each equation, both equations hold true. Therefore, the correct answer is 'TRUE'.

Tags

CCSS.8.EE.C.8B