Solve Systems of Linear Equations GraphicallyHonors Math – Grade 8

Get Ready for the Lesson

The equation y = 34.2 – 14.9x represents the number of CD singles sold (y) since the number of years after 2000 (x).The equation y = 3.3 + 4.7x represents the number of music videos (y) sold since the number of years after 2000 (x).

These two equations can be graphed on the same coordinate plane.

The point at which the graphs of the two equations intersect represents the time when the CD units sold equaled the music videos sold. The ordered pair of this point is a solution of both equations.

Two equations such as y = 34.2 – 14.9x and y = 3.3 + 4.7x together are called a system of equations.

A solution to a system of equations is an ordered pair that satisfies both equations. A system can have no, one or an infinite amount of solutions.

If the graphs intersect or coincide, the system is said to be consistent.

If a consistent system has one solution it is said to be independent. If it has infinite solutions it is dependent.

If the graphs are parallel, the system of equations is said to be inconsistent.

Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.

35

xyxy

Since the graphs are intersecting, there is one solution.

8225

yxxy

Since the graphs are parallel, there is no solution.

Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.

1425

xyxy

Since the graphs are intersecting, there is one solution.

8224

yxxy

Since the graphs coincide, there are infinitely many solutions.

Graph each system of equations. Then determine if the system has one solution, no solution, or infinitely many solutions. If the system has one solution, name it.

748

xyxy Graph each

equation separately.

Since the equation y = –x + 8 is in slope intercept form. Use the slope and the y-intercept to graph the line.

Since the equation y = 4x – 7 is in slope intercept form. However, the given graph does not have the intercept of -7. Make a chart.

The graphs intersect at (3, 5). Check to see if the solution satisfies both equations.

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Graph each system of equations. Then determine if the system has one solution, no solution, or infinitely many solutions. If the system has one solution, name it.

44262

yxyx Graph each

equation separately.

Remember the shortcut for standard form…The slope is –A/BThe y-intercept is C/B

Graph the intercept of 3 and use the slope -1/2 to find other points on the line.

Graph the intercept of 1 and use the slope -1/2 to find other points on the line.

The graphs are parallel. There is no solution.

Graph each system of equations. Then determine if the system has one solution, no solution, or infinitely many solutions. If the system has one solution, name it.

3232

yxxy Graph each

equation separately.

Since the equation y = –2x – 3 is in slope intercept form. Use the slope and the y-intercept to graph the line.

Remember the shortcut for standard form…The slope is –A/BThe y-intercept is C/B

Notice that the slope and the y-intercept are the same as the other line.

These lines coincide, therefore there are infinitely many solutions.

Graph each system of equations. Then determine if the system has one solution, no solution, or infinitely many solutions. If the system has one solution, name it.

23

1

43

1

xy

xyGraph each equation separately.

Since the equation y = –1/3x + 4 is in slope intercept form. Use the slope and the y-intercept to graph the line.

Since the equation y = 1/3x + 2 is in slope intercept form. Use the slope and the y-intercept to graph the line.

The lines intersect at (3, 3). Check to see that this ordered pair satisfies both equations in the system.