Graphing Systems of Equations

Front

What is a system of equations?

Back

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

Front

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

Back

The coordinates of the intersection point represent the solution to the system of equations.

Front

What is the solution to a system of equations when the lines are parallel?

Back

There is no solution, as parallel lines never intersect.

Front

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

Back

The system of equations has infinitely many solutions.

Front

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

Back

By finding the point(s) where the lines intersect on the graph.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does it mean if a system of equations has exactly one solution?

Back

The two lines intersect at exactly one point.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes (positive or negative).

Front

How do you find the slope of a line given two points?

Back

Use the formula: slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.