Solving Systems by Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

Solving a system of equations by graphing involves plotting the equations on a coordinate plane and identifying the point(s) where they intersect.

Front

What is the graphical representation of a linear equation?

Back

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

Front

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

Back

The solution to a system of equations graphically is found at the intersection point(s) of the lines representing the equations.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the values of the variables that satisfy all equations in the system simultaneously.

Front

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

Back

If two lines are parallel, it means there is no solution to the system, as the lines never intersect.

Front

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

Back

If two lines coincide, it means there are infinitely many solutions, as every point on the line is a solution to the system.

Front

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

Back

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

Front

How can you determine the slope of a line from a graph?

Back

The slope of a line can be determined by calculating the rise over run between two points on the line.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form.