Find the three ordered pairs (for each) satisfying the following equations -
1 - x + 2y = 5 and 2x + 4y = 17
2 - 2x + 3y = 10 and 4x +6y = 20

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Solution

$x + 2 y = 5 . . . . (1) 2 x + 4 y = 17 or x + 2 y = \frac{17}{2} . . . . (2) But equation 1 and 2 cannot be true simultaneously so it is not satisfied by any value and has no solution . 2) 2 x + 3 y = 10 . . . . . (1) 4 x + 6 y = 20 or 2 x + 3 y = 10 . . . . . (2) Since equation 1 and 2 are same so it has infinitely many solutions .$

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Condition satisfied by the pair of equation $2 x + 3 y = - 5$ and $4 x + 6 y - 10 = 0$ is

Q. Fill in the blank:
The pair of equations

2 x + 3 y = 2

and

4 x + 6 y = 1

have ________.

Q. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(i)

x + y = 5, 2 x + 2 y = 10

(ii)

x - y = 8, 3 x - 3 y = 16

(iii)

2 x + y - 6 = 0, 4 x - 2 y - 4 = 0

(iv)

2 x - 2 y - 2 = 0, 4 x - 4 y - 5 = 0

Which of the following pairs of linear equations is inconsistent?
$1. x + 3 y - 5 = 0, 2 x + y = 0$
$2. 2 x + y = 1, 2 y = 2 - 4 x$
$3. 2 x - y = 2, 2 y - 4 x = 2$

Condition satisfied by 2x +3y = -5 and 4x +6y -10 = 0 is

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Find the three ordered pairs (for each) satisfying the following equations - 1 - x + 2y = 5 and 2x + 4y = 17 2 - 2x + 3y = 10 and 4x +6y = 20

x+2y = 5....12x+4y = 17 or x+2y = 172....2But equation 1 and 2 cannot be true simultaneously so it is not satisfied by any value and has nosolution.2)2x+3y= 10 .....14x+6y= 20 or 2x+3y = 10 .....2Since equation 1 and 2 are same so it has infinitely many solutions.

Find the three ordered pairs (for each) satisfying the following equations -
1 - x + 2y = 5 and 2x + 4y = 17
2 - 2x + 3y = 10 and 4x +6y = 20