Answer:
They charged <u>$6</u> for washing and <u>$2</u> for vacuuming the car.
Step-by-step explanation:
Let the charge of washing a car be 'x'.
And also let the charge of vacuuming a car be 'y'.
Now according to question, Trisha raised $38 washing 5 cars and vacuuming 4 cars.
So framing the above sentence in equation form, we get;
![5x+4y=38\ \ \ \ \ equation\ 1](https://tex.z-dn.net/?f=5x%2B4y%3D38%5C%20%5C%20%5C%20%5C%20%5C%20equation%5C%201)
Again according to question, Byron raises $28 by washing 4 cars and vacuuming 2 cars.
So framing the above sentence in equation form, we get;
![4x+2y=28\ \ \ \ \ equation\2](https://tex.z-dn.net/?f=4x%2B2y%3D28%5C%20%5C%20%5C%20%5C%20%5C%20equation%5C2)
Now multiplying equation 2 by '2', we get;
![2(4x+2y)=28\times2\\\\8x+4y=56\ \ \ \ equation\ 3](https://tex.z-dn.net/?f=2%284x%2B2y%29%3D28%5Ctimes2%5C%5C%5C%5C8x%2B4y%3D56%5C%20%5C%20%5C%20%5C%20equation%5C%203)
Now we subtract equation 1 from equation 3 and get;
![(8x+4y)-(5x+4y)=56-38\\\\8x+4y-5x-4y=18\\\\3x=18\\\\x=\frac{18}{3}=6](https://tex.z-dn.net/?f=%288x%2B4y%29-%285x%2B4y%29%3D56-38%5C%5C%5C%5C8x%2B4y-5x-4y%3D18%5C%5C%5C%5C3x%3D18%5C%5C%5C%5Cx%3D%5Cfrac%7B18%7D%7B3%7D%3D6)
Now substituting the value of 'x' in equation 1, we get;
![5x+4y=38\\\\5\times6+4y=38\\\\30+4y=38\\\\4y=38-30=8\\\\y=\frac{8}{4}=2](https://tex.z-dn.net/?f=5x%2B4y%3D38%5C%5C%5C%5C5%5Ctimes6%2B4y%3D38%5C%5C%5C%5C30%2B4y%3D38%5C%5C%5C%5C4y%3D38-30%3D8%5C%5C%5C%5Cy%3D%5Cfrac%7B8%7D%7B4%7D%3D2)
Hence They charged <u>$6</u> for washing and <u>$2</u> for vacuuming the car.