systems practice w/applications

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 can you determine if a point (x, y) is a solution for the system y = -x + 5 and y = 2x - 7?

Back

Substitute x and y into both equations. If both equations are true, then (x, y) is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

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

Back

It means there is one unique solution to the system of equations.

Front

What does it mean if two lines are parallel on a graph?

Back

It means there is no solution to the system of equations.

Front

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

Back

It means there are infinitely many solutions to the system of equations.

Front

How do you solve a system of equations by graphing?

Back

Graph each equation on the same coordinate plane and identify the point(s) of intersection.

Front

What is the substitution method in solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the other.