1.
Answer:
In Point Form: (x,y,z)= (3,6,-1)
In Equation Form: x=3, y=6, z=-1
Step-by-step explanation:
1) Solve for x
2x+2z=4 (Subtract 2z from both sides)
-2z -2z
2x= 4-2z (Divide 2 from both sides)
/2 /2
x=2-z
2) Substitute 2-z for x in
-x-y-z=-8
-(2-z)-y-z=-8
-2+z-y-z=-8 (Combine Like Terms)
-2-y=-8 (Add 2 to both sides)
+2 +2
-y=-6 (Divide -1 from both sides)
/-1 /-1
y=6
3) Substitute 2-z for x & 6 for y in
-4x+4y+5z+=7
-4(2-z)+4(6)+5z=7 (Get rid of parentheses)
-8+4z+24+5z=7 (Combine Like Terms)
9z+16=7 (Subtract 16 from both sides)
-16 -16
9z+=-9 (Divide 9 from both sides)
/9 /9
z=-1
4) Now find x by substituting -1 for z in
x=2-z
x=2-(-1)
x=2+1
x=3
Therefore the answer is:
In Point Form: (x,y,z)= (3,6,-1)
In Equation Form: x=3, y=6, z=-1
2. Answers:
In Point Form: (x,y,z)= (1,1,0)
In Equation Form: x=1, y=1, z=0
Step-by-step explanation:
-2x + 2y + 3z = 0 (1)
-2x - y + z = -3 (2)
2x + 3y + 3z = 5 (3)
Solve (1) and (2)
Multiply 2 by 2
-2x + 2y + 3z = 0
-4x -2y + 2z = -6
-6x + 5 z = -6 (4)
Solve (2) and (3)
Multiply 2 by 3
-6x - 3y + 3z = -9
2x + 3y + 3z = 5
-4x + 6z = -4 (5)
Solve (4) and (5)
Multiply (4) by 2 and (5) by -3
-12x + 10 z = -12
12x - 18z = 12
-6z = 0
z = 0
Then
-4x + 6(0) = -4
-4x = -4
x = -4/-4
x = 1
Finally
-2(1) - y + (0) = -3
-2 - y = -3
-y = -3 + 2
y = 1
Therefore the answer is:
In Point Form: (x,y,z)= (1,1,0)
In Equation Form: x=1, y=1, z=0
