Topics:Topic 1: Solving Linear EquationsTopic 2: Solving Quadratic EquationsTopic 3: Solving Proportions involving linear and quadratic functions.Topic 4: Solving Absolute Value Equations

We want to use this information to solve linear, quadratic, and absolute value equations.

Before you start solving, you should know what type of equation you are working with and the number and type of solutions that are possible.

After you finish, you should also be able to check to see if you answer is correct or not! There should be no mystery as to whether you are right!!!

3x – 4 = 5

Graph: y = 3x – 4

Graph: y = 5

Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x,

y).

Solution: (3, 5)

3x = 9

x = 3

When we are solving equations what exactly are we doing?

When we are solving equations we are finding the x-value of the intersection of two graphs.

3(x – 4) + 5 = -4

Graph: y = 3(x - 4) + 5

Graph: y = -4

Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x,

y).

Solution: (1, -4)

3(x – 4) = -9

x – 4 = -3

x = 1

2(x + 2)2 – 8 = -6

Graph: y = 2(x + 2)2 - 8

Graph: y = -6

Solution: (-3, -6) and (-1, -6)

Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x,

y).

2(x + 2)2 = 2

(x + 2)2 = 1

x + 2 = 1

x + 2 = -1

x = -1 x = -3

-(x - 3)2 + 8 = 8

Graph: y = -(x - 3)2 + 8

Graph: y = 8

Solution: (3, 8)

Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x,

y).

-(x - 3)2 = 0

(x -3)2 = 0

x - 3 = 0

x = 3

x2 + 3 = 1

Graph: y = x2 + 3

Graph: y = 1

Solution: No Solution

Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x,

y).

x2 = -2

No Solution

½lx + 3l - 5 = -1

Graph: y = ½lx + 3l - 5

Graph: y = -1

Solution: (5, -1) and (-11, -1)

Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x,

y).

½lx + 3l = 4l x + 3 l = 8

x + 3 = 8 x + 3 = -8

x = 5 x = -11

-3l x l + 5 = 5

Graph: y = -3l x l + 5

Graph: y = 5

Solution: (0, 5)

Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x,

y).

-3l x l = 0

l x l = 0

x = 0

l x + 4 l - 3 = -6

Graph: y = l x + 4 l - 3

Graph: y = -6

Solution: No Solution

Solution of a SystemThe place where two (or more) graphs intersect is the solution of the system. The solution is written as an ordered pair (x,

y).

l x + 4 l = -3

No Solution