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Question 64589This question is from textbook ALGEBRA 1
: How do you solve linear equations and inequalities of two variables?
How do you graph linear equations of two variables?
This question is from textbook ALGEBRA 1
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! QUESTION:
A system of equations is a collection of two or more equations with the same set of unknowns.
ANSWER:
In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.
A system of linear equations can be solved four different ways:
Substitution,
Elimination,
Matrices,
Graphing.
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Let's discuss these methods with an example,
1. Solve these equations.
x-y = 4____________________________(1)
3x + 2y = 7___________________________(2)
METHOD OF SUBSTITUTION:
(1)==> x = 4 + y ___________________________(3)
Substitute this value of x in (2)
==> 3(4+ y) + 2y = 7
==> 12 + 3y + 2y = 7
==> 12 + 5y = 7
==> 5y = 7 - 12
==> 5y = -5
==> y = -5/5
==> y = -1
Now put y = -1 in (3)
==> x = 4 + -1
==> x = 3
So Solution is x = 3 and y = -1
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METHOD OF ELIMINATION:
x-y = 4____________________________(1)
3x + 2y = 7___________________________(2)
Multiply equation(1) by '2' so that coefficient of y in both equations become same( but opposite sign). Also we could make coefficient of x same.
==> 2x-2y = 8____________________________(3)
3x + 2y = 7___________________________(2)
Now add (3) and (2)
==> 2x-2y + 3x + 2y = 8 + 7
==> 5x = 15
==> x = 15/5
==> x = 3
Now substitute value of x=3 in (1)
==> 3-y = 4
==> 3- 4 = y
==> -1 = y
That is x= 3 and y = -1
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METHOD OG GRAPHING.
x-y = 4____________________________(1)
3x + 2y = 7___________________________(2)
First of all rewrite the equation in terms of 'x'
(1)==> y = x-4
Now give arbitrary values to 'x' like 0,1,2,3,...-1, -2,....(atleast 5 values)
and find out corresponding values of y.
for example, if we put x = 0, y = 0-4 = -4
if x = 1, y = 1-4= -3......and so on
Now plot these ordered pairs....
Similarly,
(2)==> 2y = 7 - 3x
==> y = 7/2 - (3/2)x
Here also give values to x and find out corresponding values of y and then plot the graph.
The resulting graph will come like this,
We can see that two straight lines intersect at a single point.
Find out the coordinates of this point.
For that draw lines perpendicular to x axis and Y axis.
The perpendicular lines will meet the X axis at 3 and in the Y axis at -1
Which gives the soluton of these equations, that is,
x = 3 and y = -1
Hope you understood.
Regards.
Praseena.
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