Solving Systems of Equations (ALL 3 Methods!)

Front

What are the three methods for solving systems of equations?

Back

1. Graphing 2. Substitution 3. Elimination

Front

How do you solve a system of equations using the substitution method?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the first variable.

Front

What does it mean if a system of equations has an infinite number of solutions?

Back

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

Front

What is the graphical interpretation of a system of equations?

Back

The solutions to the system are represented by the points where the graphs of the equations intersect.

Front

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

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

Front

What is the elimination method for 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 is the first step in solving the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

You can use either substitution or elimination; for elimination, you might multiply the second equation to align coefficients.

Front

What does the ordered pair (x, y) represent in the context of systems of equations?

Back

It represents the solution to the system, indicating the values of x and y that satisfy both equations.

Front

What is the significance of the intersection point of two lines in a graph of a system of equations?

Back

The intersection point represents the solution to the system, where both equations are satisfied.

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the values of x and y back into both original equations to see if they hold true.