Final answer:
The values of x and y are; x = 6, y = 3
Explanation:
In order to find the values of x and y in the given equation of 11y+19=8x+96, we need to follow the basic principles of solving equations. The first step is to isolate the variables on one side of the equation and the constant terms on the other side. In this case, we can start by subtracting 19 from both sides, which will give us 11y=8x+77. Next, we can divide both sides by 11 to get rid of the coefficient of y, which gives us y=(8/11)x+7.
Now, to find the value of x, we need to substitute the value of y in the equation with the given value of 3. This will give us 3=(8/11)x+7. We can then subtract 7 from both sides to get -4=(8/11)x. To find the value of x, we need to multiply both sides by the reciprocal of 8/11, which is 11/8. This will give us x=-4*(11/8)=-11/2=-5.5. Therefore, the value of x is -5.5.
To find the value of y, we can substitute the value of x in the original equation. This will give us 11y+19=8*(-5.5)+96. Simplifying this, we get 11y+19=-44+96=52. Next, we can subtract 19 from both sides to get 11y=52-19=33. Dividing both sides by 11, we get y=3. Therefore, the value of y is 3.
In conclusion, the values of x and y in the given equation of 11y+19=8x+96 are x=-5.5 and y=3. By following the basic principles of solving equations, we were able to isolate the variables and find their values. It is important to note that when dividing both sides by a coefficient, we must also divide the constant term by the same coefficient. This ensures that the equation remains balanced and we can find the correct values of the variables.