Task: Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more linear equations with the same set of variables.

Front

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

Back

It means there are no values for the variables that satisfy all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of each equation plotted on the same coordinate plane.

Front

What does it mean if two lines intersect at a point on a graph?

Back

It means the system of equations has one solution, which is the point of intersection.

Front

What is the significance of parallel lines in a system of equations?

Back

Parallel lines indicate that the system has no solution, as they never intersect.

Front

What is a unique solution in the context of systems of equations?

Back

A unique solution is when there is exactly one pair of values (x, y) that satisfies all equations in the system.

Front

What is an infinite number of solutions in a system of equations?

Back

An infinite number of solutions occurs when the equations represent the same line, meaning every point on the line is a solution.

Front

How can you determine the solution of a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where the lines intersect.

Front

What does the term 'consistent' mean in relation to systems of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.