Question

(c) Graph of equation 3x +2y = 7 and 9x - 6y

= 21 represent
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Answer 1

Given :-

Two equations i.e 3x + 2y = 7 and 9x - 6y = 21

To Find :-

The graph of the equations shows which type of lines .

Used Concepts :-

• A general linear equation in two variables is in the form of " ax + by + c = 0 ".
• For two linear equations in two variables i.e " a1x + b1y = c1 = 0 " and " a2x + b2y + c2 = 0 ".

1. The graph of the equations shows intersecting lines if and only a1/a2≠ b1/b2
2. The graph of the equations shows parallel lines if and only a1/a2=b1/b2≠c1/c2 .
3. The graph of the equations shows coincidence lines if and only a1/a2=b1/b2=c1/c2.

Solution :-

Let , 3x + 2y = 7

3x + 2y - 7 = 0

Here , a1 = 3 , b1 = 2 and c1 = -7

Again Let , 9x - 6y = 21

9x - 6y - 21 = 0

Here , a2 = 9 , b2 = -6 and c2 = -21

Therefore , a1/a2 = 3/9 = 1/3 ----- ( i )

b1/b2 = 2/-6 = -1/3 ----- ( ii )

So , a1/a2≠b1/b2

Hence , By ( i ) and ( ii ) , The pair of linear equations show intersecting lines and the lines are consistent .

Additional Information :-

• If the lines are parallel then , they are inconsistent .
• If the lines are coincidence then , they are dependent and consistent .
• If the lines are intersecting then , they are consistent .