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 you to solve for the other variable.

Front

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

Back

A system has no solution if the equations represent parallel lines, which means they have the same slope but different y-intercepts.

Front

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

Back

A system 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 substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

In the equation y = 2x + 1, what is the slope?

Back

The slope is 2.

Front

What is the y-intercept of the equation y = 4x - 1?

Back

The y-intercept is -1.

Front

How can you tell which variable to eliminate in the elimination method?

Back

You can choose to eliminate the variable that will make the calculations simpler, often the one with coefficients that are easier to work with.

Front

What is the solution to the system of equations 3x - 2y = 12 and 2x + 2y = -2?

Back

The solution is (2, 3).

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, resulting in infinitely many solutions.