1) Find all solutions to the system of equations:
x + 2y + z + w = 1
2x + 5y + 4z + w = 3
x + 3y + 2z + w = 1
2x + y + z + 2w = 2
how should i go about this???...help will b greatly appreciated. Equation 1:
x + 2y + z + w = 1
Equation 3:
x + 3y + 2z + w = 1
Multiply both sides by -1
-1*(x + 3y + 2z + w) = -1*(1)
-x - 3y - 2z - w = -1
Add to equation 1
x + 2y + z + w - x - 3y - 2z - w = 1 - 1
- y - z = 0
Solve for z
-y = z
z = -y
Equation 4:
2x + y + z + 2w = 2
Equation 1:
x + 2y + z + w = 1
Multiply both sides by -2
-2 *(x + 2y + z + w) = -2 * (1)
-2x - 4y - 2z - 2w = -2
Add to equation 4
2x + y + z + 2w - 2x - 4y - 2z - 2w = 2 - 2
-3y - z = 0
Plug in z from earlier z = -y
-3y - (-y) = 0
-3y + y = 0
-2y = 0
y = 0
Now find z
z = -y
z = -(0)
z = 0
Equation 1:
x + 2y + z + w = 1
x + 2(0) + 0 + w = 1
x + w = 1
Solve for x
x = 1 - w
Equation 2
2x + 5y + 4z + w = 3
2x + 5(0) + 4(0) + w = 3
2x + w = 3
Plug in x from earlier x = 1 - w
2(1 - w) + w = 3
2 - 2w + w = 3
-w = 3 - 2
-w = 1
w = 1 / -1
w = -1
Find x
x = 1 - w
x = 1 - (-1)
x = 1 + 1
x = 2
I hope this helped
Kia