# What is the point of contact of y = 3x + 4 and 8x - 4y = 16

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The co-ordinates of the point at which the lines y = 3x + 4 and 8x - 4y = 16 intersect satisfies both the equations.

Substituting y = 3x + 4 in 8x - 4y = 16

=> 8x - 4(3x + 4) = 16

=> 8x - 12x - 16 = 16

=> -4x = 32

=> x = -8

y = -20

**The point of intersection of the lines is (-8, -20)**

To determine the point of contact of the lines y = 3x + 4 and 8x - 4y = 16 solve the system of equations formed by the equations of the lines.

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

8x - 4y = 16 ...(2)

4*(1) + (2)

4y + 8x - 4y = 12x + 16 + 16

8x = 12x + 32

-4x = 32

x = -8

Substituting x = -8 in y = 3x + 4 gives y = -8*3 + 4 = -24 + 4 = -20

The point of intersection of the lines is (-8. -20)