
Amanda M.
asked 05/28/20Find (or predict) the intersections of the following planes:
A) x-2y+5z=10
2x + y = 10
B)4x+y-z
x-z=-12
2x+y+z=4
Please include steps and answer
1 Expert Answer

Taylor D. answered 05/28/20
Experienced Tutor Specializing in Math and Engineering
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
Amanda M.
That equation equals 005/28/20
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Taylor D.
Need more info on the first equation of part B in order to answer.05/28/20