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**Welcome to Class !!**

*We are eager to have you join us !!*

*In today’s Mathematics class, We will be looking at Simultaneous Equations. We hope you enjoy the class!*

**GRAPHICAL METHOD OF SOLVING SIMULTANEOUS EQUATION**

Expressions in x written as ax+b where a and b are constants (which can be any number) are known as linear expression. Thus we can draw a graph representing the above expression by equating it to y. To draw a linear graph we select suitable values of x so as to calculate the values of the corresponding y. hence to draw a simultaneous equation, we make y the subject in each of the equation. Then find the values of the corresponding y with the selected suitable values of x.

Steps in using the graphical method

- Make y the subject in each equation.
- Draw a table of values for each of the linear equations; taking a range of values.
- On a graph paper label the x-axis and y-axis according to the table drawn in step 2(two) above.
- Plot these values and join the points for each of the table of values.
- Take note of the point of intersection of the two lines. At this point trace it to both y and x-axes. The values are the only pair of values that satisfy both simultaneous equations.

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**Example**:

Solve graphically the simultaneous equation below

X + y =6 ; 3x –y = 12.

Solution:

- From eq (1) y= 6- x

From eq (2) y= 3x+2

- Draw the table of values of the equations taking a range of values i.e.

Table for y = 6-x

X | -1 | 0 | 1 | 2 | 3 |

y | 7 | 6 | 5 | 4 | 3 |

Guiding equation: Y=6-x

- when x= -1, Y =6-(-1), Y= 6 +1, Y=7
- when x=0, Y= 6-0, Y= 6
- when x=1, Y= 6-1, Y= 5
- when x=2, Y= 6 -2, Y= 4
- when x=3, Y=6-3, Y= 3

Table for Y=3x+2

Guiding equation: Y=3x+2

X | -1 | 0 | 1 | 2 | 3 |

y | -1 | 2 | 5 | 8 | 11 |

- when x=-1, Y=3(-1) + 2; Y= -3+2; Y= -1
- when x= 0, Y= 3(0) + 2; Y= 0+2 = 2
- when x=1, Y=5
- when x=2, Y=8
- when x=3, Y=3(3) +2; Y=9+2=11

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**EVALUATION**

- What is a linear equation?
- Which of these equations are linear? A. a+b B.a
^{2}+b =12 C. x-1 = 2 - What is the first step in drawing graph?

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__Further exercises on the use of a __**graph to solve a simultaneous equation**

when making the table of values for points to be plotted, x is called the independent variable while y is the dependent variable. The point where the variable crosses an axis is called an intercept.

Example:

Draw the graph of the given pair of the equation 2x-y=3, x+y=6 and show the point of intercept of the lines on the y-axis.

**Solution:**

- Make y the subject in each equation. I.e. Y=2x-3; Y=6-x
- Make a table of values for each equation with ranges of Y=2x-3

X | -1 | 0 | 1 | 2 | 3 |

y | -5 | -3 | -1 | 1 | 3 |

- Make the table of value for Y=6-x

X | -1 | 0 | 1 | 2 | 3 |

y | 7 | 6 | 5 | 4 | 3 |

From the graph, the points of intercept are -3 and -6.

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**EVALUATION**:

Solve graphically the below simultaneous equation:

- Y-x = -4; Y+3x =12
- 8c +3d = 1; 4c+5d =9

*We have come to the end of this class. We do hope you enjoyed the class?*

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*In our next class, we will be talking about Geometry. We are very much eager to meet you there.*

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