Systems of Equations Graphing Practice

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 two lines to intersect on a graph?

Back

When two lines intersect on a graph, it means they have a common solution, which is the point where both equations are satisfied.

Front

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

Back

To find the solution graphically, plot both equations on the same graph and identify the point where they intersect.

Front

What is the significance of the point (0, 0) in a system of equations?

Back

The point (0, 0) is the origin and can be a solution if both equations are satisfied at this point.

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

How do you determine the slope of a line from its equation?

Back

The slope can be determined from the equation in slope-intercept form (y = mx + b) as the coefficient of x (m).

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, meaning they will never intersect and there is no solution.

Front

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

Back

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

Front

How can you write an equation for a total cost based on hourly rates?

Back

The equation can be written as C = rh + b, where C is total cost, r is the rate per hour, h is the number of hours, and b is any fixed cost.

Front

What is the solution to the system of equations y = x + 3 and y = -x - 1?

Back

The solution is (-2, 1), where the two lines intersect.