CW/HW: Solving by Elimination

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What does it mean for two lines to have the same slope but different y-intercepts?

Back

It means the lines are parallel and will never intersect, indicating that the system of equations has no solution.

Front

In the elimination method, what must be true about the coefficients of the variable being eliminated?

Back

The coefficients must be the same number with opposite signs (opposites) to effectively eliminate the variable.

Front

What is the first step in using the elimination method?

Back

Identify which variable to eliminate and manipulate the equations to align the coefficients of that variable.

Front

Back

The variable y can be eliminated first by aligning the coefficients of y.

Front

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

Back

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

Front

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

Back

If the lines represented by the equations are parallel (same slope, different y-intercepts), the system has no solution.

Front

What is the significance of the constants in a system of equations when using elimination?

Back

The constants can affect the position of the lines but do not directly influence the elimination of variables.

Front

What is the result of eliminating a variable in a system of equations?

Back

The result is a single equation with one variable, which can be solved to find the value of that variable.

Front

How do you check your solution after using the elimination method?

Back

Substitute the values of the variables back into the original equations to verify that both equations are satisfied.