if some one could solve this so i can see if i'am doing it right
8x+y+z=1
7x-2y+9z=-3
4x-6y+8z=-5
thanks
There are several methods. Show what you are doing and let us critique it.
What answers did you obtain?
To solve this system of equations, you can use the method of substitution or elimination. Let's use the method of elimination in this case.
1. Start by isolating one variable in one of the equations. Let's isolate the variable 'x' in the first equation:
8x + y + z = 1
Subtract 'y' and 'z' from both sides:
8x = 1 - y - z
Divide both sides by 8:
x = (1 - y - z) / 8
2. Now substitute this value of 'x' into the other two equations to eliminate the variable 'x'.
Substituting x in the second equation:
7((1 - y - z) / 8) - 2y + 9z = -3
Simplify and solve for 'y':
(7 - 7y - 7z)/8 - 2y + 9z = -3
7 - 7y - 7z - 16y + 72z = -24
-23y +65z = -31
Substituting x in the third equation:
4((1 - y - z) / 8) - 6y + 8z = -5
Simplify and solve for 'y':
(4 - 4y - 4z)/8 - 6y + 8z = -5
4 - 4y - 4z - 48y + 64z = -40
-52y + 60z = -44
3. Now we have a system of two equations:
-23y + 65z = -31
-52y + 60z = -44
We can solve this system using the method of elimination.
Multiply the first equation by 52 and the second equation by 23 to have the same coefficient for y in both equations (to eliminate y):
-1196y + 3380z = -1612
-1196y + 1380z = -1012
Subtract the second equation from the first equation:
0y + 2000z = -600
Divide by 2000:
z = -600 / 2000
z = -0.3
4. Substitute this value of 'z' into one of the original equations to solve for 'y'. Let's use the first equation for simplicity:
8x + y + z = 1
8x + y - 0.3 = 1
Solve for 'y':
y = 1 - 8x + 0.3
y = 1 - 8x + 0.3
y = 0.7 - 8x
5. Finally, substitute the values of 'y' and 'z' into one of the original equations to solve for 'x'. Again, let's use the first equation:
8x + (0.7 - 8x) - 0.3 = 1
Simplify and solve for 'x':
8x + 0.7 - 8x - 0.3 = 1
0.7 - 0.3 = 1
0.4 = 1
Since the equation does not hold true, there is no solution to this system of equations.
Therefore, there is no solution to the given system of equations.