Solve:
3x + 7y + 5= 0
4x - 3y - 8 = 0
Find p; if:
px + y - 1= 0
3X+7Y+5=0.,..,..,.,..(1)
4X-3Y-8=0..,,..,.,...,..(2)
From (1) x=(-5-7y)/3..,..,..(3) put into equ (2) for x ; (-20-28y)/3-8=0 ; y=31/28=1.1 put into equ 3 for y
x=(-5-7.7)/3=-4.2
-4.2p +1.1-1=0 ; p=-0.1/-4.2
p=0.024
first times 3 ---> 9x + 21y = -15
2nd times 7 ---> 28x - 21y = 56
add them
37x = 41
x = 41/37
sub into 1st:
3(41/37) + 7y = -5
7y = -5 - 123/37 = -308/37
y = -44/37
then if px + y = 1
p(41/37) - 44/37 = 1
p = (1 + 44/37)(37/41) = 81/41
I verified the above answers, they satisfy the original equations.
37-32-2-47-81
To solve the system of equations:
3x + 7y + 5 = 0 ----(1)
4x - 3y - 8 = 0 ----(2)
We will use the method of substitution to find the values of x and y.
First, let's solve equation (1) for x in terms of y:
3x = -7y - 5
x = (-7y - 5) / 3
Now, substitute this value of x into equation (2):
4((-7y - 5) / 3) - 3y - 8 = 0
Simplifying the equation:
(-28y - 20) / 3 - 3y - 8 = 0
-28y - 20 - 9y - 24 = 0
-37y - 44 = 0
-37y = 44
y = -44 / -37
y = 4 / 3
Substitute the value of y back into equation (1):
3x + 7(4/3) + 5 = 0
3x + 28/3 + 5 = 0
3x = -28/3 - 15/3
3x = -43/3
x = (-43/3) / 3
x = -43/9
So the solution to the system of equations is x = -43/9 and y = 4/3.
Now, to find the value of p in the equation px + y - 1 = 0, substitute the values of x and y we just found:
p(-43/9) + (4/3) - 1 = 0
Simplifying the equation:
(-43/9)p + 4/3 - 1 = 0
(-43/9)p + 4/3 - 3/3 = 0
(-43/9)p + 1/3 = 0
(-43/9)p = -1/3
p = (-1/3) / (-43/9)
p = -1/3 * 9/43
p = -9/129
p = -3/43
Therefore, the value of p is -3/43.