graphing systems

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

A point is a solution if it satisfies all equations in the system.

Front

How do 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 a system of equations?

Back

The graphical representation consists of the lines of each equation plotted on the same coordinate plane.

Front

What does it mean if two lines intersect on a graph?

Back

It means that there is a unique solution to the system of equations at the point of intersection.

Front

What does it mean if two lines are parallel?

Back

If two lines are parallel, they have no points in common, meaning the system has no solution.

Front

What does it mean if two lines coincide?

Back

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

Front

How can you find the intersection point of two lines algebraically?

Back

Set the equations equal to each other and solve for x, then substitute back to find y.

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 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.