51 + 2z + 8z = 23
Collect 'like terms'
51 + 10z = 23
Subtract '51' from both sides
10z = 23 - 51 = -28
z = -28 /10
z = - 2.8
NB However, you have NOT indicated the mathematical signs !!!!!
(-3) x (-2z - 7) = 6z + 21 = 3 (2z + 7)
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
8
x+2y-6=z -z -z x+2y-z-6=0 +6 +6 ---------> x+2y-z=6 3y-2z=7 ---------> 0x+3y-2z=7 4+3x=2y-5z -3x -3x ---------> -3x+2y-5z=4 Put them into a matrix, for x,y,z and their answers. Solve for [A]-1[B], and the answer comes to: x= 1.75, y= 1.5, and z= -1.25
Without an equality sign the given terms can't be considered to be an equation.
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
Solve this system of equations. 5x+3y+z=-29 x-3y+2z=23 14x-2y+3z=-18 Write the solution as an ordered triple.
To solve the equation (2z + 1 - 3 = z - 2), first simplify the left side: (2z - 2 = z - 2). Next, subtract (z) from both sides to get (2z - z - 2 = -2), which simplifies to (z - 2 = -2). Finally, add 2 to both sides to find (z = 0).
2z+6z+24=0 8z+24=0 8z= -24 z= - 3
(2-r)e-rr
2z - 5 = 11 Add 5 to both sides: 2z = 16 Divide both sides by 2: z = 8
3x 3y + 6z = 12
x=3 y=2 z=6
(-3) x (-2z - 7) = 6z + 21 = 3 (2z + 7)
2z+9.75-7z=-5.15
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
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".