Solving Systems of Equations by Elimination

What is the first step in the elimination method when coefficients are not opposites?

• Multiply one or both equations to adjust coefficients

• Subtract the equations directly

• Graph the equations to find the intersection

• Use substitution method instead

What is required to start the elimination process in solving systems of equations?

• Coefficients of one variable must be opposites

• Both equations must have the same number of terms

• Ensure both equations are in the standard form

• Convert all terms to one side of the equation

What happens when you multiply an equation by a negative number in the context of elimination?

• The equation becomes undefined

• It reverses the signs of all coefficients and constants

• No changes occur to the equation

• It eliminates all variables immediately

How do you determine which variable to eliminate first in an equation?

• Choose based on which variable is easiest to isolate

• Eliminate the variable with the highest coefficient

• It depends on the coefficients and the desired simplification

• Always eliminate the variable that appears first alphabetically

After manipulating equations for elimination, what is the next step to find the solution for a variable?

• Divide the equations

• Substitute one variable into another equation

• Plot the equations on a graph

• Add or subtract the equations as needed

What is the result of adding two manipulated equations where the coefficients of one variable are opposites?

• It results in an identity like 1=1

• The variable gets doubled

• The variable is eliminated

• A new equation with higher degree terms is formed

In a real-world problem, if you have two products with different prices, how would you form the equations?

• Ignore the prices and focus on quantities only

• Multiply the quantities by each other

• Assign a variable to each product and use their quantities as coefficients

• Use the prices as coefficients

In the context of a word problem involving sales, what does each equation typically represent?

• The profit made from sales

• The difference in quantities sold

• The total cost of items sold

• The relationship between different items' sales

What does it mean if, after elimination, you are left with a statement like 0=0?

• The system has no solution

• The system has exactly one solution

• The system has infinitely many solutions

• The equations are incorrectly formed

What does a system of equations with no solution imply about the graphs of the equations?

• The graphs intersect at infinitely many points

• The graphs are the same line

• The graphs do not intersect

• The graphs intersect at one point