SOLUTION: How do you solve linear equations and inequalities of two variables? How do you graph linear equations of two variables?

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.

___________________________________________________________________________

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

________________________________________________________________________________

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

______________________________________________________________________________

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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