Final answer:
The planes 4x + 5y + 5z = 1 and 4x + 5z = 0 intersect at the line with the equation y + z = -1/5.
Step-by-step explanation:
The question asks to consider the planes 4x + 5y + 5z = 1 and 4x + 5z = 0. To find the point(s) at which these two planes intersect, we can set the equations equal to each other and solve for the unknown variables.
By doing so, we eliminate the variable 'y'. We acquire 4x + 5y + 5z = 1 = 4x + 5z = 0. Subtracting 4x from both sides, we obtain 5y+ 5z = -1. Simplifying further, we divide both sides by 5: y + z = -1/5. So, the planes intersect at the line with the equation y + z = -1/5.