Solving Systems by Elimination

Solve the following system of equations using the elimination method: 2x + 3y = 8 and 4x - 3y = 10.

• x = 5

• x = 2

• x = 3

• x = 10

What is the first step in solving a system of equations by elimination?

• Subtract one equation from the other

• Solve for one variable before eliminating the other

• Make sure that the coefficients of one of the variables are opposites

• Add the two equations together

When using the elimination method, what should be the goal when adding or subtracting the equations?

• Multiply both equations

• Divide both equations

• Add both equations

• Eliminate one of the variables

Solve the system of equations using the elimination method: 3x - 2y = 7 and 2x + 5y = 1.

• The solution for the system of equations is x = 5 and y = 1.

• The solution for the system of equations is x = 3 and y = -2.

• The solution for the system of equations is x = 2 and y = -5.

• The solution for the system of equations is x = -3 and y = 2.

What is the next step after adding or subtracting the equations in the elimination method?

• Multiply the equations

• Divide the equations

• Graph the equations

• Solve for the remaining variable

Determine whether the system of equations has no solution, one solution, or infinitely many solutions: 4x + 2y = 10 and 2x + y = 5.

• Two solutions

• Three solutions

• No solution

• One solution

What is the key concept behind the elimination method for solving systems of equations?

• Multiplying both equations together

• Eliminating one variable to solve for the other

• Dividing both equations by a constant

• Adding both equations together

Solve the following system of equations using the elimination method: 5x - 3y = 11 and 3x + 2y = 5.

• x = 3, y = 2

• x = 2, y = 4

• x = 5, y = 1

• x = 7, y = -3

What is the purpose of multiplying one or both equations by a constant in the elimination method?

• To confuse the person solving the system

• To waste time and effort

• To make the equations look more complicated

• To create opposite coefficients for one of the variables, making it easier to eliminate that variable when adding or subtracting the equations.

Explain the difference between substitution and elimination methods for solving systems of equations.

• Elimination method involves adding or subtracting the equations to eliminate one variable.

• Substitution method involves randomly substituting values into the equations.

• Elimination method involves solving one equation for one variable and then substituting that value into the other equation.

• Substitution method involves solving one equation for one variable and then substituting that value into the other equation.