Systems of Equations Elimination Multiplication

What does it mean if a system of equations has infinitely many solutions?

• It means that the equations represent the same line, and every point on that line is a solution.

• It means that the equations have no solutions at all.

• It means that the equations intersect at exactly one point.

• It means that the equations represent parallel lines that never meet.

What is a system of equations?

• A set of two or more equations with the same variables, where the solution is the point(s) where the equations intersect.

• A single equation that can be solved for one variable.

• A collection of unrelated equations that do not share any variables.

• An equation that has no solutions.

What is a common mistake when using the elimination method?

• Forgetting to multiply both sides of the equation when adjusting coefficients.

• Using the wrong variable in the equation.

• Adding the coefficients instead of subtracting them.

• Ignoring the signs of the coefficients.

When using elimination, what is the purpose of multiplying an equation?

• To make the coefficients of one variable the same in both equations, allowing for elimination.

• To simplify the equation by reducing the number of terms.

• To change the equation into a quadratic form for easier solving.

• To isolate one variable completely before solving.

What happens if the two equations in a system are parallel?

• They have one solution where they intersect.

• They have no solution because they never intersect.

• They have infinitely many solutions.

• They are equivalent and represent the same line.

What is the importance of aligning equations before elimination?

• Aligning equations helps to clearly see the coefficients of each variable, making it easier to decide how to eliminate.

• Aligning equations ensures that all variables are on one side of the equation.

• Aligning equations allows for the use of the quadratic formula.

• Aligning equations is necessary to convert them into standard form.

What is the first step in the elimination method?

• To align the equations and decide which variable to eliminate.

• To substitute one variable into the other equation.

• To graph the equations on a coordinate plane.

• To find the intersection point of the equations.

What does it mean to eliminate a variable in a system of equations?

• To manipulate the equations so that one variable can be removed, allowing for easier solving of the system.

• To add a variable to the system to increase complexity.

• To replace a variable with a constant value to simplify the equations.

• To isolate one variable on one side of the equation without removing it.

What is the result of multiplying both equations in a system by a constant?

• It changes the solution of the system.

• It does not change the solution of the system; it only changes the form of the equations.

• It makes the equations inconsistent.

• It simplifies the equations without affecting the solution.

What is the elimination method in solving systems of equations?

• The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

• The elimination method requires multiplying both equations by a constant before adding them.

• The elimination method is a graphical approach to find the intersection of two lines.

• The elimination method is used to convert equations into a single variable equation.