{:[x+y=11],[x+3=y]:} Bex and Yin are running errands together. The given system of equations relates x, the number of errands Bex has to run, and y, the number of errands Yin has to run. Based on the system, which of the following statements is true? Choose 1 answer: (A) Bex has 11 more errands to run than Yin does. (B) Yin has 11 more errands to run than Bex does. (C) Bex has 3 more errands to run than Yin does. (D) Yin has 3 more errands to run than Bex does.

Question

{:[x+y=11],[x+3=y]:} Bex and Yin are running errands together. The given system of equations relates  x, the number of errands Bex has to run, and  y, the number of errands Yin has to run. Based on the system, which of the following statements is true? Choose 1 answer: (A) Bex has 11 more errands to run than Yin does. (B) Yin has 11 more errands to run than Bex does. (C) Bex has 3 more errands to run than Yin does. (D) Yin has 3 more errands to run than Bex does.

Bytelearn · Accepted Answer

Analyze Equations: Analyze the given system of equations. We have two equations: 1. x + y = 11 2. x + 3 = y We need to find the relationship between the number of errands Bex (x) and Yin (y) have to run.Substitute and Simplify: Substitute the second equation into the first equation. From the second equation, we can express y as y = x + 3. Now we substitute this into the first equation: x + (x + 3) = 11Solve for x: Solve for x. Combine like terms: 2x + 3 = 11 Subtract 3 from both sides: 2x = 11 - 3 2x = 8 Divide both sides by 2: x = 8 / 2 x = 4Solve for y: Solve for y using the value of x. Now that we know x = 4, we can substitute it back into the second equation to find y: y = x + 3 y = 4 + 3 y = 7Determine Relationship: Determine the correct statement based on the values of x and y. We have found that Bex (x) has to run 4 errands and Yin (y) has to run 7 errands. Since y = x + 3, it means Yin has 3 more errands to run than Bex does.

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