Solve the second equation for b in terms of a; b – a = 1, b = a + 1. Substitute this expression for b in the first equation and solve for a:

10(a + 1) – 9a = 6

10a + 10 – 9a = 6

a + 10 = 6

a = –4

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

b – (–4) = 1

b + 4 = 1

b = –3

Since a = –4 and b = –3, the value of ab = (–4)(–3) = 12.

First, simplify the first equation by multiplying (a + 3) by ¹⁄₂. The first equation becomes ¹⁄₂(a) +
³⁄₂ – b = –6. Subtract ³⁄₂ from both sides, and the equation becomes ¹⁄₂(a) – b= –\(\frac{15}{2}\).Then,multiply the equation by –6 and add it to the second equation. The a terms will drop out, and you can solve for b:

–6(¹⁄₂(a) – b = –\(\frac{15}{2}\)) = –3a + 6b = 45

b = 10

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

3a – 2(10) = –5

3a – 20 = –5

3a = 15

a = 5

Since a = 5 and b = 10, the value of a + b = 5 + 10 = 15.

First, simplify the first equation by subtracting 4 from both sides. The first equation becomes 3x = –5y + 4. Then, multiply the equation by –3 and add it to the second equation. The x terms will drop out, and you can solve for y:

–3(3x = –5y + 4) = –9x = 15y – 12

–4y = –20

y = 5

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

9x + 11(5) = –8

9x + 55 = –8

9x = –63

x = –7

Since y = 5 and x = –7, the value of y – x = 5 – (–7) = 5 + 7 = 12.

First, multiply (n + 2) by –6: –6(n + 2) = –6n – 12. Then, add 12 to both sides of the equation. The first equation becomes m – 6n = 4. Add the two equations. The n terms will drop out, and you can solve for m:

m = 10

Substitute the value of m into the second equation and solve for n:

6n + 10 = 16

6n = 6

n = 1

Since m = 1 and n = 10, the value of \(\frac{n}{m}=\frac{1}{10}\).

Solve the second equation for y in terms of x; –x – y = –6, –y = x – 6, y = –x + 6. Substitute this expression for y in the first equation and solve for x:

–5x + 2(–x + 6) = –51

–5x – 2x + 12 = –51

–7x + 12 = –51

–7x = –63

x = 9

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

–9 – y = –6

–y = 3

y = –3

Since x = 9 and y = –3, the value of xy = (9)(–3) = –27.

Multiply the first equation by –6 and add it to the second equation. The x terms will drop out, and you can solve for y:

–6(^x⁄₃ – 2y = 14) = –2x + 12y = –84

y = –5

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

2x + 6(–5) = –6

2x – 30 = –6

2x = 24

x = 12

Since x = 12 and y = –5, the value of x – y = 12 – (–5) = 12 + 5 = 17.

Divide the second equation by 2 and add it to the first equation. The b terms will drop out, and you can solve for a:

\(\frac{(6a-12b=-6)}{2}=3a-6b=-3\)

a = 3

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

4(3) + 6b = 24

12 + 6b = 24

6b = 12

b = 2

Since a= 3 and b= 2,the value of a+ b= 3 + 2 = 5.

Solve the second equation for c in terms of d; c – 6d = 0, c = 6d. Substitute this expression for c in the first equation and solve for d:

\(\frac{c-d}{5}-2=0\)

\(\frac{6d-d}{5}-2=0\)

\(\frac{5d}{5}-2=0\)

d – 2 = 0

d = 2

Substitute the value of d into the second equation and solve for c:

c – 6(2) = 0

c – 12 = 0

c = 12

Since c = 12 and d = 2, the value of ^c⁄_d = \(\frac{12}{2}\) = 6.

Solve the second equation for n in terms of m; m – n = 0, n = m. Substitute this expression for n in the first equation and solve for m:

m(n + 1) = 2

m(m + 1) = 2

m² + m = 2

m² + m – 2 = 0

(m + 2)(m – 1) = 0

m + 2 = 0, m = –2

m – 1 = 0, m = 1

Multiply the first equation by 8 and add it to the second equation. The x terms will drop out, and you can solve for y:

8(¹⁄₂(x) + 6y = 7) = 4x + 48y = 56

y = 2