Algebra 3

Warm – Up 1.8

Graph.

y = 3x – 6

Algebra 3

Lesson 1.8

Objective: SSBAT solve a system of equation by graphing.

Standards: M11.D.2.1.4

What does it mean to say the ordered pair (3, 13) is a solution to the equation y = 2x + 7?

When you put the 3 in for x and the 13 in for y into the equation you get a true statement.

13 = 2(3) + 7

13 = 13

Give 1 solution to each equation using its graph.

1. y = -7x – 5

(-1, 2)

This is only 1 there are an infinite number of solutions

2. 3 2

x y

Any 1 of these is correct:

(-6, 0)

(-4, 1)

(-2, 2)

(0, 3)

(2, 4)

(4, 5)

(6, 6)

Review: A graph of an equation shows all the ordered pairs that are Solutions to that equation.

The graphs for the equations y = 3x-2 and y= -x – 6 are shown.

What ordered pair is a solution to both equations?

(-1, -5)

Continued: What does that mean…

(-1, -5) is a solution to y = 3x – 2 and it is a solution to y = -x – 6

-5 = 3(-1) – 2

-5 = -3 – 2

-5 = -5

Checks.

-5 = -(-1) – 6

-5 = 1 – 6

-5 = -5

Checks.

System of Equations

A set of 2 or more equations that use the same variables.

We use a brace to keep the equations together. Example:

32

3

xy

xy

Linear System – All equations are linear equations.

Solution of a System of Equations

An ordered pair(s) that makes ALL of the equations true

(It is a solution to all of the equations)

Solving a System of Equations through Graphing

1. Graph both equations on the same axes

2. The point(s) where the graphs intersect is the solution.

You want to draw your lines as accurate as possible use a ruler

Examples: Solve each System of Equations by Graphing.

1.

3

1

xy

xy

1st: Graph each on the same coordinate plane

Continued:

3

1

xy

xy

2nd: Find the point of intersection.

(1, -2)

This is the solution to the system of equations – it is a point on BOTH graphs.

To Check: Put the solution point into both equations and see if it works.

3

1

xy

xy (1, -2)

-2 = -1 – 1

-2 = -2

Yes.

-2 = 1 – 3

-2 = -2

Yes.

It has to work for both to be correct.

2.

2

82

xy

xy

The solution is (2, 4)

Solving a Systems of Equations on Graphing Calculator

1. Go to y= (top left of your calculator)

2. Enter one equation into y1

3. Enter the other equation into y2

4. Hit GRAPH (top right of your calculator

5. Hit 2nd, TRACE (beside the graph key)

6. Choose the INTERSECT option

7. When you get back to the screen with the graphs, hit ENTER 3 times

3.

52

21

yx

xy

Solve for y first

y = 2x – 1

y = -2x + 5

Solution: (1.5, 2)

4.

3

1226

y

yx

y = -3x + 6

y = 3 is a horizontal line through 3

Solution is (1, 3)

5.

408

32

xy

xy

y = 3x – 2 y =

Solution is (2.24, 4.72)

6.

79

59

xy

xy

No Solution These are parallel lines, which do not intersect. Therefore there is no shared ordered pair so there is no solution to the system of equations.

102

45

yx

xy

7. Which ordered pair(s) are a solution to the system of equations below?

(0, -6), (3, 11), (2, 6), (4, 2)

Answer: (2, 6)

On Own:

8.

13

3

xy

yx

Solution: (1, 2)

Homework

Worksheet 1.8