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Systems of equations.doc

By Teresa Baker,2014-11-18 13:46
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Systems of equations.doc

    Systems of equations.

    Determine if the point (1, 5) is a solution to the system of equations.

5x 2y = -5 5( ) 2( ) = -5

3x 7y = - 32 3( ) 7( ) = -32

    Determine if the point (2, 4) is a solution to the system of equations.

3y 2x = - 2 3( ) 2( ) = -2

y + 2x = 8 ( ) + 2( ) = 8

Graph y = 2x 1

    Plugging in values for x we find three solutions

Let x = 0 y = 2( ) 1 (0, -1)

Let x = -1 y = 2( ) 1 (-1, -3)

Let x = 1 y = 2( ) 1 (1, 1)

    Graph.

3y = x + 1

    2

    ;15y = x

    24

    3;15y = ( ) + 1 y = ( ) 224

    3;15y = ( ) + 1 y = ( ) 224

    3;15y = ( ) + 1 y = ( ) 224

    Solve this system of Equations by Graphing

y = x + 2

    y = x 1

    y = ( ) + 2 y = ( ) 1

    y = ( ) + 2 y = ( ) 1

    y = ( ) + 2 y = ( ) 1

Solve by Graphing.

    1y = x + 2

    3

    x + 3y = 6

    1y = ( ) + 2 ( ) + 3( ) = 6

    3

    1y = ( ) + 2 ( ) + 3( ) = 6

    3

    1y = ( ) + 2 ( ) + 3( ) = 6

    3

Graph.

Equation 1: x y = 2

    Equation 2: x + y = 6

    Solve for y, get y alone, move the x term to the other side.

x y = 2 x + y = 6

Solve by Graphing.

y = x 5

2x + y = 4

Solve this system of Equations using the Substitution Method.

y = x 6

    x + y = -2

x + ( ) = -2

    Solve this system of equations using substitution. x y = - 3

    2x + 3y = - 6

Get x alone: x y = -3

2( ) + 3y = -6

    Solve this system of equations using substitution.

y 2x = 6

    2y x = 5

Get y alone, y 2x = 6

Solve.

y = 4x 5 y = x 4

2x 3y = -5 y = 2x

    Solve this system of Equations using the Addition Method.

     x + y = 8

    - x + 2y = 7

    Solve this system of Equations using the Addition Method.

3x y = 8

    x + 2y = 5

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