System of Equations - Graphing

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

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

How do you graph the equation y = mx + b?

Back

Plot the y-intercept (b) on the y-axis, then use the slope (m) to find another point.

Front

What is the slope of the line represented by the equation y = 1/2x + 2?

Back

1/2

Front

What is the y-intercept of the equation y = -3x + 9?

Back

9

Front

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

Back

Substitute the point's coordinates into each equation; if both equations are true, it is a solution.

Front

What is the graphical representation of the solution (2, 3)?

Back

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

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution, as the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

Back

It means there are infinitely many solutions, as the lines are the same.