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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineAisha is a salon owner. Yesterday, she did 22 haircuts and colored the hair of 55 clients, charging a total of $519\$519. Today, she did 11 haircut, charging a total of $47\$47. How much does Aisha charge for her services?\newlineAisha charges $\$____\_\_\_\_for a haircut and $\$____\_\_\_\_ for a coloring.

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Q. Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineAisha is a salon owner. Yesterday, she did 22 haircuts and colored the hair of 55 clients, charging a total of $519\$519. Today, she did 11 haircut, charging a total of $47\$47. How much does Aisha charge for her services?\newlineAisha charges $\$____\_\_\_\_for a haircut and $\$____\_\_\_\_ for a coloring.
  1. Define Variables: Let xx be the cost of a haircut and yy be the cost of coloring. We can write two equations based on the given information:\newline11) 2x+5y=5192x + 5y = 519 (from yesterday's charges)\newline22) 1x+0y=471x + 0y = 47 (from today's charge for one haircut)
  2. Create Augmented Matrix: To solve using an augmented matrix, we'll write the coefficients of xx and yy and the constants in a matrix form: [25∣519 10∣47]\begin{bmatrix} 2 & 5 & | & 519\ 1 & 0 & | & 47 \end{bmatrix}
  3. Perform Row Operations: Now, we'll use row operations to get the matrix into reduced row-echelon form. First, let's make the coefficient of xx in the second row a 00 by subtracting the second row from twice the first row:\newline \begin{matrix} 2 & 5 & | & 519 \ 0 & -5 & | & 425 \end{matrix}

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