How to Solve Linear Equations by Elimination

What is the primary goal when using the elimination method to solve systems of equations?

• To make the coefficients of one variable opposites

• To graph the equations

• To find the slope of the lines

• To substitute one equation into another

In the elimination method, what happens when you add two equations with opposite coefficients for a variable?

• The variable is halved

• The variable remains unchanged

• The variable is eliminated

• The variable is doubled

How can you create opposite coefficients in the elimination method if they are not already present?

• By dividing both equations by a common factor

• By multiplying one or both equations by a number

• By adding a constant to both equations

• By subtracting one equation from the other

What is the result of adding the equations 3X + 3Y = 15 and -2X + 3Y = 85 after making the coefficients of Y opposites?

• 5X = 100

• X = 4

• 5X = 20

• X = 5

In the final example, what is the first step to eliminate the variable X?

• Divide both equations by the same number

• Subtract one equation from the other

• Multiply the equations to create opposite coefficients

• Add the equations directly

What is the solution for Y in the final example after elimination?

• Y = 5

• Y = 4

• Y = 3

• Y = 6

What is the final coordinate where the two lines intersect in the last example?

• (4, 3)

• (2, 5)

• (3, 4)

• (5, 2)