Question

The pair of linear equations 2x+3y=2 and 3x+2y=2 has solution which can be represented by a point in the co-ordinate plane in?

Answer 1

Answer:

2x + 5y = 12

We have,

x + y = 3

When y = 0 we have x = 3

When x = 0 we have y = 3

Thus we have the following table giving points on the line x + y = 3

X 0 3

Y 3 0

Now, 2 + 5y = 12

When x = 1, we have

Thus we have the following table giving points on the line 2x + 5y = 12

X 1 -4

Y 2 4

Graph of the equation x + y = 3 and 2x + 5y = 12 isClearly two lines intersect at a point P (1, 2)

Hence x = 1 and y = 2

Answer 2

The required solution of the pair of linear equations 2x+3y=2 and 3x+2y=2 is given by the point $(\frac{5}{2} ,\frac{5}{2})$in the coordinate plane.

Given :

There is a pair of linear equations 2x+3y=2 and 3x+2y=2.

To Find :

the solution of the equations as a point in the coordinate plane.

Solution :

We can find the solution to this problem in the following way.

We know that the two linear equations represent the two straight lines and the solution to these two linear equations gives the point of intersection of the two straight lines in case the straight lines are not parallel to each other.

We can solve these equations in the following way.

$2x+3y=2\\6x+9y=6\\and\\3x+2y=2\\6x+4y=4$

We can now eliminate the variable x from these two equations as follows.

$6x-6x+9y-4y=6-4\\5y=2\\y=\frac{2}{5}$

We can find the value of y in the following way.

$2x+3\times\frac{2}{5} =2\\2x=2-frac{6}{5}\\2x=frac{10-6}{5}\\x=2/5$

Therefore, the required solution of the pair of linear equations 2x+3y=2 and 3x+2y=2 is given by the point $(\frac{5}{2} ,\frac{5}{2})$in the coordinate plane.

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