Systems of Equations Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to graph a system of equations?

Back

It means to plot the equations on a coordinate plane to find their intersection point(s), which represent the solution(s).

Front

Where do we start graphing if there is no constant in the equation?

Back

At the origin (0,0).

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

If two lines are parallel, what can we say about their system of equations?

Back

The system has no solution because the lines never intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

Front

How do you find the slope of a line from its equation in slope-intercept form (y = mx + b)?

Back

The slope (m) is the coefficient of x in the equation.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

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

Back

By substituting the point's coordinates into both equations and checking if they hold true.

Front

What is the graphical representation of the solution (6, -2) in a system of equations?

Back

It is the point where the two lines intersect on the graph.