Find (or predict) the intersections of the following planes:

Question

A) x-2y+5z=10

2x + y = 10

B)4x+y-z

x-z=-12

2x+y+z=4

Please include steps and answer

Answer 1

The intersection of two planes will be a line and the intersection of three planes will be a point. For this reason, in part A your answer will come out as the equation of a line, and for part B you just need to solve the three equations for x, y, and z.

A)

x-2y+5z=10 (1)

2x+y=10 (2)

Solve equation 1 for x:

x=2y-5z+10

Insert modified equation 1 into equation 2 for x:

2(2y-5z+10)+y=10

Solve for z:

4y-10z+20+y=10

-10z+5y=-10

-10z=-5y-10

z= 0.5y+1

The Answer for A is: z=0.5y+1

B)

4x+y-z=? —> What is this equation equal to?

x-z=-12

2x+y+z=4