x + y = 3 in the form y=mx+c
will be y=−x+3 ........(equation 1)
2x - 3y = 16 in the form y=mx+c
will be y=32x−316........(equation 2)
At point of intersection (equation 1) is equal to (equation 2)
−x+3=32x−316
3+516=32x+x
325=35x
Hence. x=5
From (equation 1) y=−x+3
Therefore
y=−5+3
y=−2
Hence point of intersection is (5,-2)
For perpendicular lines the product of their gradient is -1
For line y=4x−3 the gradient is 4
Let the gradient of the other line be M2
M2 x 4 = -1
M2 = -1/4
x−5y−−2=4−1
4y+8=−x+5
4y=−x−3
The equation of the line will be,
y=−41x−43
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