{:[t-5=(1)/(3)(u+15)-5],[t=(2)/(3)(u+9)]:} Which of the following accurately describes all solutions to the system of equations shown? Choose 1 answer: (A) u=-18 and t=-6 (B) u=-3 and t=4 (c) There are infinite solutions to the system. (D) There are no solutions to the system.

Question

{:[t-5=(1)/(3)(u+15)-5],[t=(2)/(3)(u+9)]:} Which of the following accurately describes all solutions to the system of equations shown? Choose 1 answer: (A)  u=-18 and  t=-6 (B)  u=-3 and  t=4 (c) There are infinite solutions to the system. (D) There are no solutions to the system.

Bytelearn · Accepted Answer

Write Equations: Write down the system of equations. We have the following system of equations: t - 5 = (1/3)(u + 15) - 5 t = (2/3)(u + 9)Simplify First Equation: Simplify the first equation. t - 5 = (1/3)(u + 15) - 5 Multiply both sides by 3 to clear the fraction: 3(t - 5) = u + 15 - 15 3t - 15 = uSubstitute and Simplify: Substitute the expression for u from the first equation into the second equation. t = (2/3)(u + 9) t = (2/3)(3t - 15 + 9) t = (2/3)(3t - 6)Simplify Second Equation: Simplify the second equation. t = (2/3)(3t - 6) Multiply both sides by 3 to clear the fraction: 3t = 2(3t - 6) 3t = 6t - 12Solve for t: Solve for t. 3t = 6t - 12 Subtract 6t from both sides: -3t = -12 Divide both sides by -3: t = 4Substitute for u: Substitute the value of t back into the first equation to solve for u. 3t - 15 = u 3(4) - 15 = u 12 - 15 = u u = -3Check Solution: Check the solution by substituting the values of u and t into both original equations. First equation: t - 5 = (1/3)(u + 15) - 5 4 - 5 = (1/3)(-3 + 15) - 5 -1 = (1/3)(12) - 5 -1 = 4 - 5 -1 = -1 (True)  Second equation: t = (2/3)(u + 9) 4 = (2/3)(-3 + 9) 4 = (2/3)(6) 4 = 4 (True)

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