Solve:

3x + 7y + 5= 0
4x - 3y - 8 = 0

Find p; if:
px + y - 1= 0

3x+7y=-5 (i)

4x-3y=8 (ii)

(i)x 4:
12x+28y=-20 (iii)

(ii)x 3:

12x-9y=24 (iv)

(iv)-(iii):
-37y=44
y=-44/37

subs y into (i):
3x+7(-44/37)=-5
3x= -5+308/37
x=148/37

3x = -185/37 + 308/37 = 123/37

x = 41/37

To solve the system of equations:

3x + 7y + 5 = 0 ... (Equation 1)
4x - 3y - 8 = 0 ... (Equation 2)

Let's first eliminate one variable by multiplying one of the equations by a constant so that the coefficients of either x or y will cancel out when added with the other equation.

Let's start by eliminating y.

Multiply Equation 1 by 3 and Equation 2 by 7:

(3)(3x + 7y + 5) = 0 becomes 9x + 21y + 15 = 0 ... (Equation 3)
(7)(4x - 3y - 8) = 0 becomes 28x - 21y - 56 = 0 ... (Equation 4)

Now, add Equation 3 and Equation 4:

(9x + 21y + 15) + (28x - 21y - 56) = 0

Combine like terms:

9x + 28x + 21y - 21y + 15 - 56 = 0

37x - 41 = 0

Now, isolate x:

37x = 41
x = 41/37

x = 1.1081 (rounded to four decimal places)

Next, substitute the value of x back into one of the original equations to solve for y. Let's use Equation 1:

3x + 7y + 5 = 0

Plug in x = 1.1081:

3(1.1081) + 7y + 5 = 0

Simplify:

3.3243 + 7y + 5 = 0

Combine like terms:

7y + 8.3243 = 0

Isolate y:

7y = -8.3243
y = -8.3243/7

y = -1.1892 (rounded to four decimal places)

Now, let's move on to the second part of the question:

We need to find p if:

px + y - 1 = 0

Substitute the values of x = 1.1081 and y = -1.1892:

p(1.1081) + (-1.1892) - 1 = 0

Simplify:

1.1081p - 1.1892 - 1 = 0

Combine like terms:

1.1081p - 2.1892 = 0

Add 2.1892 to both sides:

1.1081p = 2.1892

Now, isolate p:

p = 2.1892 / 1.1081

p = 1.9731 (rounded to four decimal places)

Therefore, the value of p is approximately 1.9731.