System of Equations from Graphs

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 for a system of equations to have one solution?

Back

It means the lines representing the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines representing the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

It means the lines representing the equations are the same line, thus intersecting at every point on the line.

Front

How can you find the solution to a system of equations graphically?

Back

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

Front

What is the significance of the x-axis and y-axis in a graph of a system of equations?

Back

The x-axis typically represents the independent variable, while the y-axis represents the dependent variable.

Front

If two lines intersect at (3, 5), what is the solution to the system of equations?

Back

The solution is (3, 5).

Front

What does it indicate if two lines on a graph are parallel?

Back

It indicates that the system of equations has no solution.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

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

Back

By substituting the point's coordinates into each equation to see if they hold true.