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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineSubstitute teachers with Newport School District get paid by the day, although subs with teaching credentials earn a different amount than subs without credentials. Yesterday, 11 credentialed sub taught in the district. That cost the district $89\$89. Today, 99 non-credentialed subs and 1111 credentialed subs taught, receiving $1,528\$1,528 from the district. How much do subs get paid?\newlineSubs without credentials get paid ____\_\_\_\_ per day, and subs with credentials get paid ____\_\_\_\_ per day.

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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.\newlineSubstitute teachers with Newport School District get paid by the day, although subs with teaching credentials earn a different amount than subs without credentials. Yesterday, 11 credentialed sub taught in the district. That cost the district $89\$89. Today, 99 non-credentialed subs and 1111 credentialed subs taught, receiving $1,528\$1,528 from the district. How much do subs get paid?\newlineSubs without credentials get paid ____\_\_\_\_ per day, and subs with credentials get paid ____\_\_\_\_ per day.
  1. Define Variables: Let xx be the daily pay for subs without credentials and yy be the daily pay for subs with credentials. From the first day, we have the equation y=89y = 89. From the second day, we have the equation 9x+11y=15289x + 11y = 1528.
  2. Write System of Equations: Now we write the system of equations:\newline11. y=89y = 89\newline22. 9x+11y=15289x + 11y = 1528
  3. Create Augmented Matrix: To solve using an augmented matrix, we rewrite the system as:\newline11. 0x+1y=890x + 1y = 89\newline22. 9x+11y=15289x + 11y = 1528\newlineAnd the augmented matrix is:\newline\begin{bmatrix}0 & 1 | & 89\9 & 11 | & 1528\end{bmatrix}
  4. Eliminate Variable yy: Since the first equation only contains yy, we can use it to eliminate yy from the second equation. Multiply the first equation by −11-11 and add it to the second equation:\newline−11×[01∣89]=[−0−11∣−979]-11 \times [0 1 | 89] = [-0 -11 | -979]\newline[911∣1528]+[−0−11∣−979]=[90∣549][9 11 | 1528] + [-0 -11 | -979] = [9 0 | 549]
  5. New System of Equations: Now we have the new system of equations:\newline11. y=89y = 89\newline22. 9x=5499x = 549
  6. Solve for x: Divide the second equation by 99 to solve for x:\newline9x9=5499\frac{9x}{9} = \frac{549}{9}\newlinex=61x = 61

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