solve this system of equations and solve for triple pair:
x+y+z=8
2y+4y+2z=26
-x+8y-3z=26
I think your second equation is probably
2x+4y+2z=26
add the first and third ---> 9y - 2z = 34 (#1)
multiply third by 2
-2x + 16y - 6z = 52
add that to the second
20y -4z = 78
10y - 2z = 39 (#2)
#2 - #1 : ----> y = 5
sub into #1
45 - 2z = 34
-2z = -11
z = 5.5
back into the first
x + 5 + 5.5 = 8
x = -2.5
x = -2.5
y= 5
z = 5.5
To solve this system of equations, we will use the method of substitution.
Step 1: Rearrange the first equation to solve for x:
x = 8 - y - z
Step 2: Substitute the value of x in the second and third equations:
2y + 4y + 2z = 26 (equation 2)
-(8 - y - z) + 8y - 3z = 26 (equation 3)
Simplify equation 2:
6y + 2z = 26
Simplify equation 3:
-8 + y + z + 8y - 3z = 26
9y - 2z = 34
Step 3: Solve the simplified system of equations:
Now we have a system of two equations with two variables:
6y + 2z = 26 (equation 4)
9y - 2z = 34 (equation 5)
Multiply equation 4 by 3 and equation 5 by 2 to eliminate the variable z:
18y + 6z = 78 (equation 6)
18y - 4z = 68 (equation 7)
Subtract equation 7 from equation 6:
(18y + 6z) - (18y - 4z) = 78 - 68
18y + 6z - 18y + 4z = 10
10z = 10
z = 1
Step 4: Substitute the value of z back into one of the equations to solve for y:
Using equation 4:
6y + 2(1) = 26
6y + 2 = 26
6y = 24
y = 4
Step 5: Substitute the values of y and z back into one of the equations to solve for x:
Using the original equation:
x + y + z = 8
x + 4 + 1 = 8
x + 5 = 8
x = 3
Therefore, the solution to the system of equations is x = 3, y = 4, and z = 1.