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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.
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
EVALUATION
- What is a linear equation?
- Which of these equations are linear? A. a+b B.a2 +b =12 C. x-1 = 2
- What is the first step in drawing graph?
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.
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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