Solve the first equation for a in terms of b by multiplying both sides of the equation by 2. a = 2b + 2. Substitute this expression for a in the second equation:

3(2b + 2 – b) = –21

3(b + 2) = –21

3b + 6 = –21

3b = –27

b = –9

Substitute the value of b into the first equation and solve for a:

^a⁄₂ = –9 + 1

^a⁄₂ = –8

a = –16

Since a = –16 and b = –9, the value of \(\sqrt{\frac{a}{b}}=\sqrt{\frac{-16}{-9}}=\sqrt{\frac{16}{9}}=\frac{4}{3}\)

First, simplify the first equation by multiplying (x – 1) by 9: 9(x – 1) = 9x – 9. Then, add 9 and 4y to both sides of the equation. The first equation becomes 9x + 4y = 11. Then, multiply the second equation by –2 and add it to the first equation. The y terms will drop out, and you can solve for x:

–2(2y + 7x = 3) = –4y – 14x = –6

x = –1

Substitute the value of x into the second equation and solve for y:

2y + 7(–1) = 3

2y – 7 = 3

2y = 10

y = 5

Since y = 5 and x = –1, the value of (y – x)² = (5 – (–1))² = 6² = 36.

Multiply the second equation by 3 and add it to the first equation. The p terms will drop out, and you can solve for q:

3(–5p + 2q = 24) = –15p + 6q = 72

q = 7

Substitute the value of q into the second equation and solve for p:

–5p + 2(7) = 24

–5p + 14 = 24

–5p = 10

p = –2

Since p = –2 and q = 7, the value of (p + q)² = (–2 + 7)² = 5² = 25.

First, simplify the second equation by subtracting 9 from both sides of the equation. The second equation becomes –2x – 6 = y. Then, multiply the equation by 2 and add it to the first equation. The x terms will drop out, and you can solve for y:

2(–2x – 6 = y) = –4x – 12 = 2y

y = 6

Substitute the value of y into the first equation and solve for x:

4x + 6 = –3(6)

4x + 6 = –18

4x = –24

x = –6

Since x = –6 and y = 6, the value of ^x⁄_y = –⁶⁄₆ = –1.

Solve the second equation for y in terms of x; 2x –y = 9, –y = –2x + 9, y = 2x – 9. Substitute this expression for y in the first equation and solve for x:

\(\frac{x+2x-9}{3}=9\)

\(\frac{3x-9}{3}=8\)

x – 3 = 8

x = 11

Substitute the value of x into the second equation and solve for y:

2(11) – y = 9

22 – y = 9

–y = –13

y = 13

Since x = 11 and y = 13, the value of x – y = 11 – 13 = –2.