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Q: How do you solve the equation. X2 plus y2 plus z2 - 4x plus 4y plus 2z plus 5 equals 0 x2 plus y2 plus z2 equals 4?

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By including its plus or minus signs

Solve this system of equations. 5x+3y+z=-29 x-3y+2z=23 14x-2y+3z=-18 Write the solution as an ordered triple.

2z+6z+24=0 8z+24=0 8z= -24 z= - 3

2z+9.75-7z=-5.15

60j + 2z = 6

4z + 3 = 6 + 2zSubtract 2z from each side of the equation:2z + 3 = 6Subtract 3 from each side:2z = 3Divide each side by 2:z = 3/2 = 1.5

x=3 y=2 z=6

Without an equality sign the given terms can't be considered to be an equation.

The answer to 2Z plus 9.75 subtract 7Z subtract equals 14.90. This is a math problem.

y=5x+2 if y equals -4

13y+3z+8

-2z + 3

9-4z2 = (3-2z)(3+2z)

3x 3y + 6z = 12

3z + 8 + 2z + 6 = 5z + 14

z = 3.6

1st equation: x-y-z = 0 2nd equation: 2x-y+2z = 1 3rd equation: x-y+z = -2 They appear to be simultaneous equations dependent on each other for the solutions which are: x = 4, y = 5 and z = -1

2z+17=21 subtract 17 from both sides. 2z=4 divide both sides by 2 z=2

4x + 3y + 2z = 34; 2x + 4y + 3z = 45; 3x + 2y + 4z = 47 First, eliminate terms in z from 2 of the equations, by muliplying first equation by 2 and subtracting third equation from the answer: 8x + 6y + 4z = 68, subtract leaving 5x + 4y = 21 (equation 4) Similarly multiply the first equation by 3 and the second by 2 giving 12x + 9y + 6z = 102 and 4x + 8y + 6z = 90 Subtract again and we have 8x + y = 12 or y = 12 - 8x Substitute this in equation 4 gives 5x + 4(12 -8x) = 21 Simplify: 5x + 48 - 32x = 21 = -27x = -27 so x = 1 y = 12 - 8x so y = 4 and in one of the original equations 4 + 12 + 2z = 34, ie 2z = 34 -16 so z =9 Check: 2x + 4y + 3z = 2 +16 + 27 = 45 and 3x + 2y + 4z = 3 + 8 + 36 = 47 QED!

2z - 5 = 11 Add 5 to both sides: 2z = 16 Divide both sides by 2: z = 8

(-3) x (-2z - 7) = 6z + 21 = 3 (2z + 7)

I used the matrix method to find the answer: x=4, y=-7, z=-5.

The matrix is singular because the last equation is the same as the second equation (simply multiplying every term in an equation by the same number (in this case, 2) does not produce an equation with new information). for example 1) 3x=3y 2) 2x=2y has no useful solution beyond the information from 1) that x=y You would get a singular matrix for this. The Gauss-Jordan method will not solve equations which cannot be solved by the old "elimination method".

9z + 10 - 6z = 7 + 2z - 3 gather together z terms on the left 3z + 10 = 7 + 2z - 3 gather integers on the right 3z + 10 = 2z + 4 subtract 2z from each side z + 10 = 4 subtract 10 from each side z = - 6 ----------------check in original equation 9(- 6) + 10 - 6(- 6) = 7 + 2(- 6) - 3 - 54 + 10 + 36 = 7 - 12 - 3 - 8 = - 8 --------------checks

1st equation: x-y-z = 0 2nd equation: 2x-y+2z = 1 3rd equation: x-y+z = -2 Multiply all terms in 1st equation by 3 then add all equations together:- So: 6x-5y = -1 Multiply all terms in 3rd equation by 2 and subtract it from the 2nd equation:- So: y = 5 Therefore by means of substitution: x = 4, y = 5 and z = -1