Algebra 6-1 Entry Ticket - Graphing Systems of Equations

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 on a graph.

Front

What does it mean for a coordinate to be a solution to a system of equations?

Back

A coordinate is a solution to a system of equations if it satisfies all equations in the system when substituted for the variables.

Front

How do you graph the equation y = -x + 5?

Back

To graph y = -x + 5, start at the y-intercept (0, 5) and use the slope of -1 to find another point, such as (1, 4).

Front

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

Back

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

Front

What is the y-intercept of the equation y = 2x - 7?

Back

The y-intercept is -7, which is the point where the line crosses the y-axis.

Front

What does it mean if a system of equations has no solution?

Back

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

Front

What does it mean if a system of equations has many solutions?

Back

A system has many solutions if the equations represent the same line, meaning they intersect at infinitely many points.

Front

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

Back

Substitute the x and y values of the point into each equation. If both equations are true, the point is a solution.

Front

What is the graphical representation of the solution to a system of equations?

Back

The solution is represented by the point(s) where the graphs of the equations intersect.

Front

What is the first step in solving a system of equations graphically?

Back

The first step is to graph each equation on the same coordinate plane.