Simultaneous Equations: Elimination Method

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.

In the equation 3x + 2y = 10, what is the coefficient of x?

• 7

• 5

• 2

• 3

Answer explanation

The coefficient of x in the equation 3x + 2y = 10 is 3, as it is the number directly multiplied by x.

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.

In the equation 5x - 4y = 20, what is the coefficient of y?

• 5

• -4

• 4

• 20

Answer explanation

The coefficient of y in the equation 5x - 4y = 20 is -4 because it is the number directly multiplied by y.

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.

Identify the coefficients in the equation 4x - 3y = 12

• 5 and -2

• 2 and -3

• 4 and 3

• 4 and -3

Answer explanation

The coefficients in the equation 4x - 3y = 12 are 4 and -3, as they are the numbers multiplying the variables x and y respectively.

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.

Explain the process of solving for variables in simultaneous equations using the elimination method.

• Divide the equations to eliminate one variable, then solve for the remaining variable.

• Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

• Ignore one of the equations and solve for the remaining variable in the other equation.

• Multiply the equations to eliminate one variable, then solve for the remaining variable.

Answer explanation

Add or subtract the equations to eliminate one variable, then solve for the remaining variable.

In the equation 6x + 5y = 30, what is the coefficient of x?

• 11

• 6

• 5

• 30

Answer explanation

The coefficient of x in the equation 6x + 5y = 30 is 6, as it is the number multiplied by x in the equation.