(4, 2)
(4, -2)
(-4, 2)
(-4, -2)
Correct answer is A
The point of intersection for the two lines exists at the point where the two lines are equal to each other. Make anyone of the variables the subject of the formula and equate the two lines to each other and solve for the coordinates of the point of intersection.
Given lines 2y+3x−16=0 and 7y−2x−6=0 , making x the subject of the formula:
Line 1 : 2y+3x−16=0⟹3x=16−2y
∴
Line 2 : 7y - 2x - 6 = 0 \implies -2x = 6 - 7y
\therefore x = \frac{7}{2}y - 3
Equating them together and solving, we have:
\frac{16}{3} - \frac{2}{3}y = \frac{7}{2}y - 3 \implies \frac{16}{3} + 3 = \frac{7}{2}y + \frac{2}{3}y
\frac{25}{3} = \frac{25}{6}y \therefore y = 2
Putting y = 2 in the equation 3x = 16 - 2y, we have
3x = 16 - 2(2) = 16 - 4 = 12 \implies x = 4
The coordinate of P is (4, 2).
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