Elimination Method Different Coefficients

-4x - 6y = -24

4x - 7y = - 54

Let's combine (add) these 2 equations to ELIMINATE the x variable. What would our combined equations be?

• -1y = 30

• 13y = -30

• -1y = -78

• -13y = -78

The coefficients of the eliminated variable must be _____.

• opposites

• the same

• distinct

• does not matter

If a student wanted to use elimination on this problem, what would they have to do first?

• Divide by 4 in the first equation

• Isolate the variables on both equations

• Subtract 8y from the first equation

• Add 3 to the second equation

Which of the four methods would you use to solve this by elimination?

• Method 1 (Subtract the equations)

• Method 2 (Add the equations)

• Method 3 (Criss-cross coefficients and subtract)

• Method 4 (Criss-cross coefficients and add)

The process of adding or subtracting scales of one equation from another is called

• Substitution

• Elimination

• Graphing

• Guessing

What is the first step in using the elimination method to solve simultaneous equations?

• Subtract one equation from the other

• Add the two equations together

• Divide both equations by a common factor

• Make the coefficients of one of the variables the same in both equations

Answer explanation

The first step in using the elimination method is to make the coefficients of one of the variables the same in both equations.

Solve the following system of equations using the elimination method: 2x + 3y = 11 and 4x - 2y = 6

• x = 2.5, y = 2

• x = 2, y = 2.5

• x = 5, y = 2

• x = 2, y = 4

Answer explanation

To solve the system of equations, multiply the first equation by 2 to eliminate y. Then subtract the second equation from the first to find x. Substitute x back to find y. The correct solution is x = 2.5, y = 2.

Using the elimination method, solve the system of equations: 3x - 2y = 16 and 2x + 2y = 4

• The solution is x = 4 and y = -2.

• The solution is x = 0 and y = 0.

• The solution is x = -3 and y = 5.

• The solution is x = 2 and y = 3.

Answer explanation

By adding the two equations, we eliminate y, giving 5x = 20. Solving for x, we get x = 4. Substituting x back into one of the equations, we find y = -2. Therefore, the solution is x = 4 and y = -2.

What is the second step in using the elimination method to solve simultaneous equations?

• Divide the equations by a random number

• Square the equations to eliminate one of the variables

• Multiply the equations by a random number

• Add or subtract the equations to eliminate one of the variables

Answer explanation

The second step in using the elimination method is to add or subtract the equations to eliminate one of the variables, allowing you to solve for the remaining variable.

Solve the following system of equations using the elimination method: 5x + 2y = 23 and 3x - 4y = -7

• x = 3, y = 4

• x = 4, y = 5

• x = 2, y = 3

• x = 5, y = 2

Answer explanation

To solve the system of equations, multiply the first equation by 2 and the second equation by 5 to eliminate y. Then, subtract the equations to find x = 3. Substitute x back to find y = 4. Therefore, x = 3 and y = 4.