Where does the line 3x + 7y + 4 = 0 intersect the lines 3x + y = 0 and x + 6y + 2 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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To find the point of intersection of the lines 3x + 7y + 4 = 0 and 3x + y = 0, we solve the system of equations formed by the two equations.

3x + 7y + 4 = 0 ...(1)

3x + y = 0 ...(2)

From (2) substitute for y in (1)

3x + 7(-3x) + 4 = 0

=> 3x - 21x + 4 = 0

=> -18x = -4

=> x = 2/9

y = -3*(2/9) = -2/3

The point of intersection of the lines 3x + 7y + 4 = 0 and x + 6y + 2 = 0 can be found by solving the system of equations

3x + 7y + 4 = 0 ...(1)

x + 6y + 2 = 0 ...(2)

Substitute for x in (1) from (2)

=> 3(-6y - 2) + 7y + 4 = 0

=> -18y - 6 + 7y + 4 = 0

=> -11y = 2

=> y = -2/11

x = -6*(-2/11) - 2

=> 12/11 - 2 = -10/11

The point of intersection of 3x + 7y + 4 = 0 and 3x + y = 0 is (2/9, -2/3) and the point of intersection of 3x + 7y + 4 = 0 and x + 6y + 2 = 0 is (-10/11, -2/11)

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