The first of these equatiosn plus the second equals thethird: x + y + z = 2 x +

Question

The first of these equatiosn plus the second equals thethird: x + y + z = 2 x + 2y + z = 3 2x + 3y + 2z = 5 The first two planes meet along a line. The third planecontains that line, because if x, y, z satisfy the first twoequations then they also ________. The equations haveinfinitely many solutions (the whole line L). Find threesolutions of L. In the blank, I put "meet at the same line". I'm stuckon finding solutions...what is the procedure for finding asolution? Is x = 0, y = 1, z = 1 or x = 1, y = 1, z = 0 validsolutions? Thanks in advance :) The first of these equatiosn plus the second equals thethird: x + y + z = 2 x + 2y + z = 3 2x + 3y + 2z = 5 The first two planes meet along a line. The third planecontains that line, because if x, y, z satisfy the first twoequations then they also ________. The equations haveinfinitely many solutions (the whole line L). Find threesolutions of L. In the blank, I put "meet at the same line". I'm stuckon finding solutions...what is the procedure for finding asolution? Is x = 0, y = 1, z = 1 or x = 1, y = 1, z = 0 validsolutions? Thanks in advance :)

Explanation / Answer

    Given lines are     x+y+z=2    -----(1)    x+2y+z=3   -----(2) 2x+3y+2z=5 -----(3).    solving (1) and (2) we have x+z=1    solving (1) and (3) we have x+z=1    now substitute x+z=1 in equation (1),i.e.y=2-(x+z)=2-1=1.    now put z=0 in x+z=1 then x=1           putz=1in x+z=1 then x=0 the required solutions are x=1,y=1,z=0 or x=0,y=1,z=1.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.