{:[11 e-9f+1=5(f-3e)],[2f+4e=3]:} Consider the system of equations. Which of the following statements is true? Choose 1 answer: (A) There is only one solution (e,f) and e*f is positive. (B) There is only one solution (e,f) and e*f is negative. (c) There are infinitely many solutions. (D) There are no solutions.

Question

{:[11 e-9f+1=5(f-3e)],[2f+4e=3]:} Consider the system of equations. Which of the following statements is true? Choose 1 answer: (A) There is only one solution  (e,f) and  e*f is positive. (B) There is only one solution  (e,f) and  e*f is negative. (c) There are infinitely many solutions. (D) There are no solutions.

Bytelearn · Accepted Answer

Write system of equations: Write down the system of equations. We have the following system of equations: 1) 11e - 9f + 1 = 5(f - 3e) 2) 2f + 4e = 3Simplify first equation: Simplify the first equation. Expand the right side of the first equation: 11e - 9f + 1 = 5f - 15e Now, move all terms involving variables to one side and constants to the other side: 11e + 15e = 5f + 9f - 1 Combine like terms: 26e = 14f - 1Express e in terms of f: Express e in terms of f. Divide both sides by 26 to solve for e: e = (14f - 1) / 26Substitute expression for e: Substitute the expression for e into the second equation. Replace e in the second equation with the expression found in Step 3: 2f + 4((14f - 1) / 26) = 3Simplify second equation: Simplify the second equation. Multiply through by 26 to clear the fraction: 26(2f) + 4(14f - 1) = 26(3) 52f + 56f - 4 = 78 Combine like terms: 108f - 4 = 78Solve for f: Solve for f. Add 4 to both sides: 108f = 82 Divide both sides by 108: f = 82 / 108 Simplify the fraction: f = 41 / 54Substitute value of f into e: Substitute the value of f back into the expression for e. e = (14(41 / 54) - 1) / 26Simplify expression to find e: Simplify the expression to find e. Multiply 14 by 41/54: e = (574/54 - 1) / 26 Subtract 1 (which is the same as subtracting 54/54): e = (520/54) / 26 Simplify the fraction: e = 20/54 / 26 e = 10/27Check solution in original equations: Check the solution in both original equations. Substitute e = 10/27 and f = 41/54 into the original equations to verify the solution: 1) 11(10/27) - 9(41/54) + 1 ?= 5(41/54 - 3(10/27)) 2) 2(41/54) + 4(10/27) ?= 3 Perform the calculations to check if both sides of the equations are equal.Determine sign of e*f: Determine the sign of e*f. Since both e and f are positive fractions, their product will also be positive.

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