{:[3(4-a)-b=5(3a-2b)+8],[3(2b-3)=7a]:} Consider the system of equations. If (a,b) is the solution to the system, then what is the value of a*b ? Choose 1 answer: (A) (7)/(3) (B) (38)/(9) (c) (59)/(9) (D) (266)/(27)

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{:[3(4-a)-b=5(3a-2b)+8],[3(2b-3)=7a]:} Consider the system of equations. If  (a,b) is the solution to the system, then what is the value of  a*b ? Choose 1 answer: (A)  (7)/(3) (B)  (38)/(9) (c)  (59)/(9) (D)  (266)/(27)

Bytelearn · Accepted Answer

Rearranging terms: Now, let's rearrange the terms to bring like terms to one side and constants to the other side. We get: 3a + 15a + b + 10b = 12 + 8. Combining like terms, we have: 18a + 11b = 20.Expanding the second equation: Next, let's expand the second equation in the system: 3(2b-3)=7a. Expanding gives us: 6b - 9 = 7a. Rearranging to express a in terms of b, we get: 7a = 6b - 9. Dividing by 7, we have: a = (6b - 9)/7.Substituting expression for a: Now, let's substitute the expression for a from the second equation into the first equation. Substituting a = (6b - 9)/7 into 18a + 11b = 20, we get: 18((6b - 9)/7) + 11b = 20. Multiplying through by 7 to clear the fraction, we have: 18(6b - 9) + 77b = 140.Solving for b: Expanding and combining like terms, we get: 108b - 162 + 77b = 140. Combining like terms again, we have: 185b - 162 = 140. Adding 162 to both sides, we get: 185b = 302.Substituting value of b into expression for a: Now, let's solve for b by dividing both sides by 185. We get: b = 302/185. Simplifying the fraction, we have: b = 302/185.Performing operations inside parentheses: Next, we substitute the value of b back into the expression for a: a = (6b - 9)/7. Substituting b = 302/185 into a = (6b - 9)/7, we get: a = (6(302/185) - 9)/7.Calculating a and b in fraction form: Now, let's perform the operations inside the parentheses. Multiplying 6 by 302/185, we get: a = (1812/185 - 9)/7. Converting 9 to a fraction with a denominator of 185, we get: a = (1812/185 - 1665/185)/7.Multiplying a and b: Subtracting the fractions, we get: a = (147/185)/7. Now, we divide 147 by 185 and then divide the result by 7. We have: a = 147/(185*7).Simplifying the fraction: Multiplying the denominators, we get: a = 147/1295. Now, we have both a and b in fraction form.Comparing the fraction with answer choices: Finally, we multiply a and b to find a*b. Multiplying a = 147/1295 by b = 302/185, we get: a*b = (147/1295)*(302/185).Rechecking calculations: Multiplying the numerators and denominators, we get: a*b = (147*302)/(1295*185). Calculating the multiplication, we have: a*b = 44414/239675.Now, let's simplify the fraction if possible. However, 44414 and 239675 do not have common factors other than 1, so the fraction is already in its simplest form.We can now compare the fraction 44414/239675 with the given answer choices. None of the answer choices match this fraction, which indicates a possible calculation error. Let's recheck our calculations.

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