Solve systems of equations by graphing or substitution

Front

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

Back

The system has no solution if the graphs of the equations are parallel lines, meaning they never intersect.

Front

What is the solution to the system of equations represented by the lines graphed by Buzz?

Back

The solution is the point where the two lines intersect, which is (1, -4).

Front

Solve by Substitution: x = -3y - 17; 2x + 3y = -7. What is the solution?

Back

The solution is (10, -9).

Front

What point is a solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2, 5).

Front

Is the point (2, -1) a solution to the system of equations y=5x+3 and y=-2x-4?

Back

No, (2, -1) is not a solution.

Front

What does the graph of a system of equations with infinitely many solutions look like?

Back

The graph consists of two overlapping lines, indicating that every point on the line is a solution.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into both equations. If both equations are true, the point is a solution.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves graphing both equations on the same coordinate plane and identifying the point(s) of intersection.

Front

What does it mean if two lines in a system of equations are skew?

Back

Skew lines are lines that do not intersect and are not parallel, typically found in three-dimensional space.