Section 8.1

What we are Learning:To solve systems of equations by graphing

Determine if a system of equations has one solution, no solutions, or infinite solutions by graphing

System of Equations:

• Two or more equations with two or more variables in them

• They are used together to solve a problem• The solution to the system is an ordered pair

which satisfies (answers) both equations– Ordered pair: (x, y), (s, t), (m, n)….

Graphing a System of Equations:• Write each equation in slope-intercept form– Slope-intercept form: y = mx + b

• b is the y-intercept; where the line crosses the y-axis• m is the slopeExample:

• Carefully graph each equation• The point where the two equations cross is the

ordered pair which is the solution to the System.

2y – 3x = 12 +3x +3x2y = 3x + 12 2 2y = 3/2 x + 6; m = 3/2, b = 6

Example:Graph the system of equations to find the solution.

• 3x + 2y = 4-2x + 8y = 16

• Rewrite each equation in slope intercept form.

3x + 2y = 4-3x -3x2y = -3x + 4 2 2y = -3/2x + 2

-2x + 8y = 16+2x +2x8y = 2x + 16 8 8y = 2/8x + 2y = 1/4x + 2

Solution: (0, 2)

Now graph your lines!

If the Graphs of a System…

• Intersect:– There is exactly one solution– Is called Consistent– Is called Independent

• Are the Same Line:– There are infinitely many solutions– Is called Consistent– Is called Independent

• Do Not Intersect are Parallel:– There is no solution– Is called Inconsistent

Let’s Work This Together:

• 2x + y = -4 5x + 3y = -6

Solution:Number of Solutions:

Let’s Work This Together:

• y = ¼ x + 7 4y = x

Solution:Number of Solutions:

Let’s Work This Together:

• 4x + 2y = 8 3y = -6x + 24

Solution:Number of Solutions:

Homework:

• Page 459– 27 to 37 odd

Remember: Show all of your work and check your answers in the back of the book in order to receive credit!