y-4=4x+3y=-(9-x)
What is the value of xy?
what are we to make of the two = signs?
I believe it's like:
y-4=4x+3y
y-4=-(9-x)
4x+3y=-(9-x)
well, then we have
y-4 = 4x+3y
2y = -4x-4
y = -2x-2
y-4 = -(9-x)
y-4 = x-9
y = x-5
So,
-2x-2 = x-5
x = 1
and thus y = -4
xy = -4
To find the value of xy, we need to solve the given system of equations:
y - 4 = 4x + 3y
-(9 - x)
Let's simplify the equations and rearrange them to solve for y:
First equation:
y - 3y = 4x + 4
-2y = 4x + 4
Divide through by -2:
y = -2x - 2
Second equation:
9 - x = 0 - 3y
-x + 9 = -3y
Divide through by -3:
(1/3)x - 3 = y
Now we have the value of y in terms of x. We can substitute this into either of the original equations to find x or y.
Substituting y = -2x - 2 into the second equation:
(1/3)x - 3 = -2x - 2
Let's solve for x:
(1/3)x + 2x = -3 + 2
(1/3)x + (6/3)x = -1
(7/3)x = -1
Multiply through by 3 to remove the fraction:
7x = -3
x = -3/7
Now that we have the value of x, we can substitute it back into y = -2x - 2 to find y:
y = -2(-3/7) - 2
y = 6/7 - 2
y = -8/7
Therefore, the solution to the system of equations is x = -3/7 and y = -8/7. To find the value of xy, we multiply x and y together:
xy = (-3/7) * (-8/7)
xy = 24/49
Hence, the value of xy is 24/49.