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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Jackie has $2363 in her retirement account, and Edgar has $2359 in his. Jackie is adding $9 per day,whereas Edgar is contributing $11 per day. Eventually, the two accounts will contain the same amount. How long will that take? What balance will each account have? After days, Jackie and Edgar will each have a retirement account balance of $◻.

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newline Jackie has $2363\$2363 in her retirement account, and Edgar has $2359\$2359 in his. Jackie is adding $9\$9 per day, whereas Edgar is contributing $11\$11 per day. Eventually, the two accounts will contain the same amount. How long will that take? What balance will each account have? \newlineAfter days\text{days}, Jackie and Edgar will each have a retirement account balance of $□\$\square.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newline Jackie has $2363\$2363 in her retirement account, and Edgar has $2359\$2359 in his. Jackie is adding $9\$9 per day, whereas Edgar is contributing $11\$11 per day. Eventually, the two accounts will contain the same amount. How long will that take? What balance will each account have? \newlineAfter days\text{days}, Jackie and Edgar will each have a retirement account balance of $□\$\square.
  1. Define Variables: Let's define the variables:\newlineLet xx be the number of days after which both Jackie and Edgar will have the same amount in their retirement accounts.\newlineLet yy be the amount of money that both Jackie and Edgar will have in their retirement accounts after xx days.
  2. Write Equations: We can write two equations to represent the situation:\newlineFor Jackie: y=2363+9xy = 2363 + 9x (since she starts with $2363\$2363 and adds $9\$9 per day)\newlineFor Edgar: y=2359+11xy = 2359 + 11x (since he starts with $2359\$2359 and adds $11\$11 per day)
  3. Use Substitution: Now we will use substitution to solve the system of equations. Since both equations equal yy, we can set them equal to each other: 2363+9x=2359+11x2363 + 9x = 2359 + 11x
  4. Solve for x: Next, we solve for x:\newline2363+9x−9x=2359+11x−9x2363 + 9x - 9x = 2359 + 11x - 9x\newline2363=2359+2x2363 = 2359 + 2x\newline2363−2359=2x2363 - 2359 = 2x\newline4=2x4 = 2x\newlinex=42x = \frac{4}{2}\newlinex=2x = 2
  5. Find Value of y: Now that we have the value of xx, we can find the value of yy by substituting xx into one of the original equations. We'll use Jackie's equation:\newliney=2363+9(2)y = 2363 + 9(2)\newliney=2363+18y = 2363 + 18\newliney=2381y = 2381
  6. Final Result: So, after 22 days, Jackie and Edgar will each have a retirement account balance of $2381\$2381.

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