Solving Systems by 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 of a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

It means the system has no solution because the lines never intersect.

Front

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

Back

It means the system has infinitely many solutions because the lines are the same.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines: parallel lines (no solution), intersecting lines (one solution), or coinciding lines (infinitely many solutions).

Front

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

Back

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

Front

How do you find the intersection point of two lines graphically?

Back

By plotting both lines on the same graph and identifying the point where they cross.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

What is the graphical representation of the equation y = 2x + 3?

Back

A straight line with a slope of 2 and a y-intercept at (0, 3).