1. Verify the consistency of the systems given below and find a particular solution if the system is consistent: (i) 4x - 5y + z = -3 2x + 3y - z = 3 3x - y + 2z = 5 x + 2y - 5z = -9 (ii) x? + x? + x? + x? = 2 2x? - x? + 2x? - x? = -5 3x? + 2x? + 3x? + 4x? = 7 2. Find the values of \(\alpha\) and \(\beta\) such that the system x + y + z = 6 x + 2y + 3z = 10 x + 2y + \alpha z = \beta has (i) no solution (ii) infinitely many solution (iii) a unique solution.
Added by Ruben B.
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For the first system of equations, we can use the method of substitution or elimination to find the solution. Let's use the method of elimination: First, multiply the first equation by 2 and the second equation by 4 to make the coefficients of x the same in both Show more…
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Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent x−3/4y+5/4z=15/4 −1/4x+1/2y+1/8z=−19/8 −5/2+9/2y+z=−21
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Solve each system of equations. If the system has no solution, state that it is inconsistent. $$ \left\{\begin{array}{r} 2 x-3 y-z=0 \\ -x+2 y+z=5 \\ 3 x-4 y-z=1 \end{array}\right. $$
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Solve each system of equations. If the system has no solution, say that it is inconsistent. $$\left\{\begin{aligned} 2 x-3 y-z &=0 \\ 3 x+2 y+2 z &=2 \\ x+5 y+3 z &=2 \end{aligned}\right.$$
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