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in Coordinate Geometry by (47.8k points)
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(2, 1) is the point of intersection of two lines.

(1) x – y – 3 = 0; 3x – y – 7 = 0

(2) x + y = 3; 3x + y = 7

(3) 3x + y = 3; x + y = 7

(4) x + 3y – 3 = 0; x – y – 7 = 0

1 Answer

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Best answer

(2) x + y = 3; 3x + y = 7

Substitute the value of x = 2 and y = 1 in the given equation.

(1) ⇒ x – y – 3 = 0

2 – 1 – 3 = 0

2 – 4 = 0

– 2 ≠ 0

Not true

3x – y – 7 = 0

3(2) – 1 – 7 = 0

6 – 8 = 0

-2 ≠ 0

Not true

(2) ⇒ x + y = 3

2 + 1 = 3

3 = 3

True

3x + y = 7

3(2) + 1 = 7

6 + 1 = 7

7 = 7

True

∴ (2, 1) is the point of intersection

(3) ⇒ 3x + y = 3

3(2) + 1 = 3

6 + 1 = 3

7 = 3

Not true

x + y = 7

2 + 1 = 7

3 = 7

Not true

(4) ⇒ x + 3y – 3 = 0

2 + 3 – 3 = 0

5 – 3 = 0

2 ≠ 0

Not true

x – y – 7 = 0

2 – 1 – 7 = 0

2 – 8 = 0

-6 ≠ 0

Not true

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