#5.1 Solving Systems of Linear Equations by Graphing

Front

A system of linear equations is...

Back

a set of two or more linear equations in the same variable.

Front

A SOLUTION to a system of linear equations is....

Back

an ordered pair that is a solution to both equations.

Front

Is the ordered pair (2, 6) a solution to the system?

Back

Yes

Front

Solve the system by graphing: y = 2x + 4 and y = -x + 8.

Back

The solution is (2, 6).

Front

You sell bracelets for $2 each and necklaces for $3 each at a local flea market. You collect $95, selling a total of 37 jewelry items. Which system can be used to determine how many of each type of jewelry you sold?

Back

The system is: 2x + 3y = 95 and x + y = 37.

Front

What does the graph of a system of linear equations represent?

Back

The points of intersection represent the solutions to the system.

Front

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

Back

Substitute the point into both equations; if it satisfies both, it is a solution.

Front

What is the graphical method for solving a system of linear equations?

Back

Plot both equations on the same graph and identify the intersection point.

Front

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

Back

The system has no solution because the lines never intersect.

Front

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

Back

The system has infinitely many solutions because the lines are the same.