Solving Systems of Equations by Table & Graphs

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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What does it mean for two lines to intersect?

Back

It means that the two equations have a common solution, represented by the point of intersection.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

It means that the lines are parallel and never intersect.

Front

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

Back

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

Front

How can you determine the solution of a system of equations using a table?

Back

By finding the row in the table where the values of the variables are the same for both equations.

Front

What is the graphical representation of a system of equations?

Back

It is the plot of the equations on a coordinate plane, showing the lines and their intersections.

Front

What is the y-value in the solution (x, y)?

Back

It is the second number in the ordered pair that represents the solution to the system.

Front

What does it mean if two lines are coincident?

Back

It means they lie on top of each other, indicating infinitely many solutions.

Front

How do you find the x-value of the solution from a graph?

Back

By identifying the x-coordinate of the point where the two lines intersect.