if x+y=11, y+z=14, and x+z=13, what is the value of x+y+z ?
Eq1: X + Y = 11.
Eq2: Y + Z = 14.
Y = 14 - Z.
Eq3: X + Z = 13.
X = 13 - Z.
In Eq1, substitute (13-Z) for X, and
(14-Z) for Y:
(13-Z) + (14-Z) = 11,
13 - Z + 14 - Z = 11,
-2Z + 27 = 11,
-2Z = 11 - 27 = -16,
Z = 8.
X + Y + Z,
Substitute 11 for y and 8 for Z:
(X+Y)+Z = 11 + 8 = 19.
CORRECTION:
Substitute 11 for (x+y).
To find the value of x+y+z, we can solve the system of equations given.
1. Start by adding the three equations together:
(x + y) + (y + z) + (x + z) = 11 + 14 + 13
Simplifying, we get:
2x + 2y + 2z = 38
2. Divide both sides of the equation by 2:
2x + 2y + 2z = 38
(2x + 2y + 2z) / 2 = 38 / 2
Simplifying further, we get:
x + y + z = 19
Therefore, the value of x + y + z is 19.
To find the value of x+y+z, we need to solve the system of equations given.
Step 1: Let's solve for x in terms of y by rearranging the equation x+y=11:
x = 11 - y
Step 2: Let's solve for y in terms of z by rearranging the equation y+z=14:
y = 14 - z
Step 3: Substitute the values of x and y from the above equations into the equation x+z=13:
(11 - y) + z = 13
(11 - (14 - z)) + z = 13
11 - 14 + z + z = 13
-3 + 2z = 13
2z = 13 + 3
2z = 16
z = 16/2
z = 8
Step 4: Substitute the value of z into the equation y+z=14 to solve for y:
y + 8 = 14
y = 14 - 8
y = 6
Step 5: Substitute the values of y and z into the equation x+y=11 to solve for x:
x + 6 = 11
x = 11 - 6
x = 5
So, x = 5, y = 6, and z = 8.
Finally, to find the value of x+y+z:
x+y+z = 5+6+8 = 19
Therefore, the value of x+y+z is 19.