Solving Systems by graphing

Front

What is the solution to a system of equations?

Back

The solution is the point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

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

Back

The slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

If two lines are parallel, they have the same slope but different y-intercepts, resulting in no solution for the system.

Front

What does it mean if two lines are coincident?

Back

If two lines are coincident, they lie on top of each other, meaning they have infinitely many solutions.

Front

How do you find the intersection point of two lines?

Back

To find the intersection point, solve the system of equations simultaneously to find the values of the variables.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

A system has one solution if the graphs of the equations intersect at exactly one point.

Front

How can you determine if a system of equations has no solution?

Back

A system has no solution if the lines are parallel and never intersect.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on the coordinate plane.