Let's solve the problem step by step.
Given the expressions:
- [tex]\( A = 12A - 2x - 3xy + 5y\)[/tex]
- [tex]\( B = -y^2 + 5xy - x2\)[/tex]
- [tex]\( C = 7x2 - 7y^2 + xy\)[/tex]
You need to find the value of [tex]\( A - 2B + C \)[/tex] when [tex]\( x = -1 \)[/tex] and [tex]\( y = 2\)[/tex].
First let's evaluate each expression individually.
### Expression A
The expression given for [tex]\( A \)[/tex] is:
[tex]\[ A = 12A - 2x - 3xy + 5y \][/tex]
### Expression B
[tex]\[ B = -y^2 + 5xy - x2 \][/tex]
Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = 2 \)[/tex]:
[tex]\[ B = -(2)^2 + 5(-1)(2) - (-1)(2) \][/tex]
[tex]\[ B = -4 + (-10) + 2 \][/tex]
[tex]\[ B = -4 - 10 + 2 \][/tex]
[tex]\[ B = \-12 \][/tex]
### Expression C
[tex]\[ C = 7x2 - 7y^2 + xy \][/tex]
Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = 2 \)[/tex]:
[tex]\[ C = 7(-1)(2) - 7(2)^2 + (-1)(2) \][/tex]
[tex]\[ C = -14 - 7(4) + (-2) \][/tex]
[tex]\[ C = -14 - 28 - 2 \][/tex]
[tex]\[ C = -44 \][/tex]
Now, we need to calculate [tex]\( A - 2B + C \)[/tex]. Since we don't have an evaluated expression for [tex]\( A \)[/tex], we cannot proceed with the calculations. Let's assume there's another expression for [tex]\( A \)[/tex] in another context.
If [tex]\( A \)[/tex] is properly defined, we could proceed and calculate the final result. But an undefined [tex]\( A \)[/tex], means our steps cannot yield a specific numerical value. This is why defining [tex]\( A \)[/tex] correctly is crucial.
