Math  /  Algebra

QuestionSubmit Answer [-/2.3 Points] DETAILS MY NOTES TANAPMATH7 5.3.036. PRACTICE ANOTHER
Solve the system of linear equations, using the Gauss-Jordan elimination method, (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameter tt. Use ss if a second parameter is needed.) 3x2y+z=2x+3y4z=52x3y+5z=3x8y+9z=8(x,y,z)=()\begin{array}{rr} 3 x-2 y+z= & 2 \\ x+3 y-4 z= & 5 \\ 2 x-3 y+5 z= & -3 \\ x-8 y+9 z= & -8 \\ (x, y, z)=(\square) \end{array} Need Help? Read It Whatch it
Glow My Work (Optiona)

Studdy Solution
Analyze the resulting matrix:
The system has infinitely many solutions because there are free variables. Express z z in terms of a parameter t t :
Let z=t z = t .
From Row 2: y1311z=1311 y - \frac{13}{11}z = \frac{13}{11}
y=1311+1311t y = \frac{13}{11} + \frac{13}{11}t
From Row 1: 3x2y+z=2 3x - 2y + z = 2
Substitute y y and z z :
3x2(1311+1311t)+t=2 3x - 2\left(\frac{13}{11} + \frac{13}{11}t\right) + t = 2
Solve for x x :
3x=2+2611+2611tt 3x = 2 + \frac{26}{11} + \frac{26}{11}t - t
3x=4811+1511t 3x = \frac{48}{11} + \frac{15}{11}t
x=1611+511t x = \frac{16}{11} + \frac{5}{11}t
Therefore, the solution in terms of the parameter t t is:
(x,y,z)=(1611+511t,1311+1311t,t) (x, y, z) = \left(\frac{16}{11} + \frac{5}{11}t, \frac{13}{11} + \frac{13}{11}t, t\right)

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