Topic 2 Simultaneous Equations - Elimination Flashcards
Fill in the blank: To solve the system of equations 5x + 2y = 10 and 3x + 2y = 6, you can eliminate ________.
y
In the equations 5x + 3y = 15 and 10x + 6y = 30, what type of solution is present?
Infinitely many solutions.
True or False: The elimination method can be used with fractions.
True
What do you do if the coefficients of the variable to be eliminated are already equal?
Directly add or subtract the equations.
What do you do after eliminating a variable?
Solve the resulting equation for the remaining variable.
True or False: The elimination method can only be used for two equations.
False
What is the first step in the elimination method?
To manipulate the equations so that one variable can be eliminated.
What is the elimination method’s primary goal?
To simplify the system of equations to find variable values.
True or False: The elimination method is always the easiest method to solve simultaneous equations.
False
How can you check your solution after solving simultaneous equations?
By substituting the values back into the original equations.
What is the significance of the determinant in a system of equations?
It helps determine whether the system has a unique solution, no solution, or infinitely many solutions.
In the elimination method, what happens if you end up with a false statement like 0 = 5?
It indicates that the system of equations is inconsistent.
Fill in the blank: When two equations have the same slope but different y-intercepts, they are ________.
parallel
What does it mean if two equations are inconsistent?
It means there is no solution because the lines represented by the equations are parallel.
Fill in the blank: The elimination method can be especially useful when dealing with ________ coefficients.
large
What is a simultaneous equation?
A simultaneous equation is a set of equations with multiple variables that are solved together.
In the system of equations 3x + 2y = 12 and 6x + 4y = 24, what can be concluded?
The equations are dependent and represent the same line.
True or False: You can use elimination to solve equations with three variables.
True
What type of systems can be solved using the elimination method?
Linear systems.
True or False: The elimination method can yield a single unique solution.
True
Fill in the blank: The elimination method involves ________ one variable to solve for another.
eliminating
What is the purpose of multiplying an equation in the elimination method?
To create equivalent equations that allow for easy elimination of a variable.
What is a unique solution in the context of simultaneous equations?
A unique solution is when the two equations intersect at exactly one point.
In the equations 2x + 3y = 6 and 4x + 6y = 12, are the equations dependent, independent, or inconsistent?
Dependent
