Solving Systems of Linear Equations - Substitution Method

What is the purpose of the substitution method in solving systems of equations?

• To simplify the process of finding the values of the variables by reducing the number of equations.

• To eliminate one variable by adding the equations together.

• To graph the equations and find the intersection point.

• To convert the equations into a single equation with one variable.

What is the substitution method?

• A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

• A technique used to eliminate variables by adding equations together.

• A graphical method for finding the intersection of two lines.

• A process of replacing variables with constants to simplify equations.

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

• The equations represent different lines that intersect at one point.

• The equations represent the same line, meaning every point on the line is a solution.

• The equations have no solutions, meaning they are parallel lines.

• The equations represent two distinct lines that intersect at multiple points.

What is the graphical representation of a system of linear equations?

• The slope of the lines representing the equations.

• The intersection point(s) of the lines representing the equations.

• The area between the lines representing the equations.

• The distance between the lines representing the equations.

How do you isolate a variable in an equation?

• Rearranging the equation to get the variable on one side and the constants on the other.

• Multiplying both sides of the equation by the same number.

• Adding the same value to both sides of the equation without changing the variable's position.

• Dividing both sides of the equation by the variable's coefficient.

What does it mean if a system of equations has no solution?

• The lines represented by the equations are parallel and never intersect.

• The lines intersect at one point.

• The lines coincide and have infinitely many solutions.

• The lines are perpendicular to each other.

What is the first step in using the substitution method?

• Solve one of the equations for one variable in terms of the other variable.

• Multiply both equations by a common denominator.

• Add the two equations together to eliminate a variable.

• Graph both equations to find the intersection point.

How can you check your solution for a system of equations?

• Substitute the values back into the original equations to see if they hold true.

• Graph the equations and see if the lines intersect.

• Use a calculator to find the roots of the equations.

• Multiply the equations to see if they yield the same result.

What is a system of linear equations?

• A set of two or more linear equations with the same variables.

• A single linear equation with multiple variables.

• A collection of nonlinear equations.

• A system of equations that has no solutions.

What does it mean to solve a system of equations?

• Finding the values of the variables that satisfy all equations in the system.

• Identifying the number of equations in the system.

• Graphing the equations to find their intersection points.

• Eliminating one variable to simplify the equations.