Question

find the point of intersection of two lines x+y-6=0 & x-3y-2=0​

Answer 1

Given lines

• x + y - 6 = 0⠀⠀.... [1]
• x - 3y - 2 = 0⠀⠀.... [2]

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❏ Subtracting [1] from [2]

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→ (x - 3y - 2) - (x + y - 6) = 0

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→ x - 3y - 2 - x - y + 6 = 0

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→ x - x - 3y - y - 2 + 6 = 0

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→ -4y + 4 = 0

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→ -4y = -4

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→ y = -1

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❏ Substituting the value of y in [1]

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→ x + y - 6 = 0

→ x - 1 - 6 = 0

→ x - 7 = 0

→ x = 7

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We know that, solution of two lines is the intersection of both lines.

Therefore the required intersection point should be (x, y).

⠀

Hence,

• Intersection point of the given lines is (7, -1).