Solve the following systems of equations and simplify the expressions.

I. System of equations:

Given system:

\( \begin{cases} 5x - 2y = 11 \\ 4x - y = 4 \end{cases} \)

From the second equation, we can express \( y \) as \( y = 4x - 4 \).

Substitute this into the first equation:

\( 5x - 2(4x - 4) = 11 \)

\( 5x - 8x + 8 = 11 \)

\( -3x = 11 - 8 \)

\( -3x = 3 \)

\( x = -1 \)

Now substitute \( x = -1 \) back into the equation for \( y \):

\( y = 4(-1) - 4 \)

\( y = -4 - 4 \)

\( y = -8 \)

II. Simplify the expression:

Given expression:

\( (a+6)^2 - 2a(3-2a) \)

Expand the terms:

\( (a^2 + 12a + 36) - (6a - 4a^2) \)

Distribute the negative sign:

\( a^2 + 12a + 36 - 6a + 4a^2 \)

Combine like terms:

\( (a^2 + 4a^2) + (12a - 6a) + 36 \)

\( 5a^2 + 6a + 36 \)

III. System of equations:

Given system:

\( \begin{cases} 3x + 5y = 12 \\ x - 2y = -7 \end{cases} \)

From the second equation, we can express \( x \) as \( x = 2y - 7 \).

Substitute this into the first equation:

\( 3(2y - 7) + 5y = 12 \)

\( 6y - 21 + 5y = 12 \)

\( 11y = 12 + 21 \)

\( 11y = 33 \)

\( y = 3 \)

Now substitute \( y = 3 \) back into the equation for \( x \):

\( x = 2(3) - 7 \)

\( x = 6 - 7 \)

\( x = -1 \)

IV. Simplify the expression:

Given expression:

\( 2x(2x+3y) - (x+y)^2 \)

Expand the terms:

\( (4x^2 + 6xy) - (x^2 + 2xy + y^2) \)

Distribute the negative sign:

\( 4x^2 + 6xy - x^2 - 2xy - y^2 \)

Combine like terms:

\( (4x^2 - x^2) + (6xy - 2xy) - y^2 \)

\( 3x^2 + 4xy - y^2 \)

Ответ: 1. x = -1, y = -8. 2. 5a² + 6a + 36. 3. x = -1, y = 3. 4. 3x² + 4xy - y².