Question

Determine the line of intersection of each system of equations. help would be greatly appreciated :D
a.) 2x + y + z = 7
4x +3y - 3z = 13
4x _2y +2z = 14

Answer 1

1.) 2x + y + z = 7
2.) 4x +3y - 3z = 13
3.) 4x - 2y +2z = 14

Subtract Equation 3 from Equation 2 to get the line.
Then subtract Equation 1 from Equation 2 to verify.

You want to eliminate x variable in both subtractions.

Answer 2

2x + y + z = 7 -->(-2)2x + y + z = 7
4x + 3y - 3z = 13
-----------------
-4x - 2y - 2z = - 14 (result of multiplying by -2)
4x + 3y - 3z = 13
-----------------add
y - 5z = -1

4x + 3y - 3z = 13 -->(-1)4x + 3y - 3z = 13
4x - 2y + 2z = 14
----------------
-4x - 3y + 3z = - 13 (result of multiplying by -1)
4x - 2y + 2z = 14
-----------------add
- 5y + 5z = 1

y - 5z = -1
-5y + 5z = 1
--------------add
-4y = 0
y = 0/-4 = 0

y - 5z = - 1
0 - 5z = - 1
-5z = - 1
z = -1/-5 = 1/5

2x + y + z = 7
2x + 0 + 1/5 = 7
2x = 7 - 1/5
2x = 35/5- 1/5
2x = 34/5
x = (34/5)/2
x = 34/5 * 1/2
x = 34/10 = 17/5

check...
2x + y + z = 7
2(17/5) + 0 + 1/5 = 7
34/5 + 0 + 1/5 = 7
35/5 = 7
7 = 7 (correct)
check...
4x + 3y - 3z = 13
4(17/5) + 3(0) - 3(1/5) = 13
68/5 + 0 - 3/5 = 13
65/5 = 13
13 = 13 (correct)
check...
4x - 2y + 2z = 14
4(17/5) - 2(0) + 2(1/5) = 14
68/5 - 0 + 2/5 = 14
70/5 = 14
14 = 14 (correct)
ANSWER : x = 17/5, y = 0, z = 1/5 or (17/5,0,1/5)

Answer 3

@texaschic101 :

It says to determine the `line of intersection`, not the points of intersection.

Answer 4

oops

Answer 5

I think this question should have read:

If possible, determine the line of intersection of each system of equations.