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P.S: Here are the equations I worked. Feel free to point out anything that I may have done wrong.

2x+4y-1z-6k+2j=-1

3x+6y-3z-8k+4j=1

1x+3y+4z-2k+4j=47

4x-2y-2z+6k+2j=28

5x+3y+4z+3k+3j=69

(The values are X=2, Y=3, Z=5, K=4, J=6).

- Thread starter Liger20
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- #1

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P.S: Here are the equations I worked. Feel free to point out anything that I may have done wrong.

2x+4y-1z-6k+2j=-1

3x+6y-3z-8k+4j=1

1x+3y+4z-2k+4j=47

4x-2y-2z+6k+2j=28

5x+3y+4z+3k+3j=69

(The values are X=2, Y=3, Z=5, K=4, J=6).

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member 11137

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Ben Niehoff

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2x + 3y = 11

represents a line. A system of two equations

2x + 3y = 11

8x - 6y = 7

represents

Now, carry this to three dimensions:

A single linear equation like

4x + 3y - 6z = 8

represents a

4x + 3y - 6z = 8

2x - 5y + 2z = 3

would then represent two planes. Since there are fewer equations than variables, you can't solve for a unique (x,y,z); however, what you

Three equations

4x + 3y - 6z = 8

2x - 5y + 2z = 3

3x - 8y - 7z = 10

give you

Now, you can extend this upward. A linear equation with five variables

3x - 3y + 2z - 6u - 5v = 7

represents a linear 4-dimensional hyperplane; that is, it represents the analogue of a plane in 5 dimensions. If you have five such equations, then they will intersect in a single point (x,y,z,u,v), as long as no two of the hyperplanes are parallel.

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HallsofIvy

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By "intersection of the line" do you mean the line of intersection of two planes? If the planes are Ax+ By+ Cz= D and Px+ Qy+ Rx= S you can solve those two equations for two of the variables, say x or y, in terms of the third, z. If x= f(z), y= g(z), you can then write the line in parametric equations x= f(t), y= g(t), z= t. (Since a line is

If you have one equation in n variables, you can solve for

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Ben Niehoff

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Actually, my earlier statement was slightly incorrect. What really matters, is whether all of the equations are linearly independent of each other. In three dimensions, if your equations are:And how do you tell if the planes are parallel?

[tex]\begin{array}{rcl} a_1x + a_2y + a_3z & = & A \\ b1_x + b_2y + b_3z & = & B \\ c_1x + c_2y + c_3z & = & C \end{array}[/tex]

then you can find a unique solution (x,y,z) as long as the determinant

[tex]\left| \begin{array}{ccc} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{array} \right| \neq 0[/tex]

The same idea carries over into higher dimensions; if the determinant of all the coefficients is nonzero, then the solution will be a single point.

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rcgldr

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A paremetic equation relates variables to functions of another variable, such as:What is a parametric equation?

x = cos(t)

y = sin(t)

An equation with "n" multiple variables don't have to imply "n" dimensions , just "n" independent components, such as X, Y, Z, temperature, density, pressure, which has 6 components but is only 3 dimensional.

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