System of Linear Equations In Exercises 25-38, solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination.
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- Coefficient Design In Exercises 79-84, determine the values of k such that the system of linear equations has the indicated number of solutions. Exactly one solution kx+2ky+3kz=4kx+y+z=02xy+z=1arrow_forwardCoefficient Design In Exercises 79-84, determine the values of k such that the system of linear equations has the indicated number of solutions. Infinitely many solutions kx+y=163x4y=64arrow_forwardWriting Consider the system of linear equations in x and y. a1x+b1y=c1a2x+b2y=c2a3x+b3y=c3 Describe the graphs of these three equations in the xy-plane when the system has a exactly one solution, b infinitely many solutions, and c no solution.arrow_forward
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- One hundred liters of a 50% solution is obtained by mixing a 60% solution with a 20% solution. Use a system of linear equations to determine how many liters of each solution are required to obtain the desired mixture. Solve the system using matrices.arrow_forwardBack-Substitution. In Exercises 25-30, use back-substitution to solve the system. x+yz=02y+z=312z=0arrow_forwardChecking Solutions in Exercises 7-10, determine whether each ordered triple is a solution of the system of equations. 6xy+z=14x3z=192y+5z=25 (a) 0,3,1 (b) 3,0,5 (c) 0,1,4 (d) 1,0,5arrow_forward
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