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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineAt a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases 33 hot dog meals and 33 hamburger meals, paying a total of $36\$36. Mr. Hogan buys 11 hot dog meal and 33 hamburger meals, spending $26\$26 in all. How much do the meals cost?\newlineHot dog meals cost $\$_______ each, and hamburger meals cost $\$________ each.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineAt a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases 33 hot dog meals and 33 hamburger meals, paying a total of $36\$36. Mr. Hogan buys 11 hot dog meal and 33 hamburger meals, spending $26\$26 in all. How much do the meals cost?\newlineHot dog meals cost $\$_______ each, and hamburger meals cost $\$________ each.
  1. Define variables: Let's define the variables for the cost of the meals. Let xx be the cost of a hot dog meal and yy be the cost of a hamburger meal.
  2. Write equations: Write the system of equations based on the information given. Mrs. Wilkerson's purchase gives us the first equation: 3x3x (hot dog meals) + 3y3y (hamburger meals) = $36\$36. Mr. Hogan's purchase gives us the second equation: 1x1x (hot dog meal) + 3y3y (hamburger meals) = $26\$26.\newlineSo we have:\newline3x+3y=363x + 3y = 36\newlinex+3y=26x + 3y = 26
  3. Solve equations: Solve the system of equations. We can use the substitution or elimination method. Let's use the elimination method. We can multiply the second equation by −3-3 to eliminate yy.\newline−3(x+3y)=−3(26)-3(x + 3y) = -3(26)\newline−3x−9y=−78-3x - 9y = -78
  4. Eliminate variable: Now we add the new equation from Step 33 to the first equation to eliminate yy.(3x+3y)+(−3x−9y)=36+(−78)(3x + 3y) + (-3x - 9y) = 36 + (-78)3x−3x+3y−9y=36−783x - 3x + 3y - 9y = 36 - 780x−6y=−420x - 6y = -42Since 0x0x is 00, we can simplify this to:−6y=−42-6y = -42
  5. Solve for y: Solve for y by dividing both sides of the equation by -6＂).\(\newline\$-6y / -6 = -42 / -6\)\(\newline\)\(y = 7\)\(\newline\)So, the cost of a hamburger meal is \(\$7\).
  6. Substitute and solve: Substitute the value of \(y\) back into one of the original equations to solve for \(x\). We'll use the second equation: \(x + 3y = 26\).\(x + 3(7) = 26\)\(x + 21 = 26\)\(x = 26 - 21\)\(x = 5\)So, the cost of a hot dog meal is \(\$5\).

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