Solving Systems by Substitution and Elimination

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, allowing for the solution of the remaining variable.

Front

How do you determine if a system of equations has no solution?

Back

A system of equations has no solution if the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system of equations has infinitely many solutions if the equations represent the same line, meaning they have the same slope and y-intercept.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations and manipulate them (if necessary) so that adding or subtracting them will eliminate one of the variables.

Front

In the equation 4x + 4y = 4, what is the value of y when x = 0?

Back

When x = 0, substituting into the equation gives 4y = 4, so y = 1.

Front

What is the significance of the coefficients in a system of equations?

Back

The coefficients determine the slope and position of the lines represented by the equations, which affects whether the system has one solution, no solution, or infinitely many solutions.

Front

How can you check your solution after solving a system of equations?

Back

You can check your solution by substituting the values of the variables back into the original equations to see if they satisfy both equations.

Front

What is the graphical interpretation of a system of equations with one solution?

Back

Graphically, a system with one solution is represented by two lines that intersect at a single point.

Front

What is the purpose of rearranging equations in the substitution method?

Back

Rearranging equations in the substitution method allows you to express one variable in terms of the other, making it easier to substitute into the second equation.