Step One
Add the first and third
-2x + 2y + 3z = 0
2x + 3y + 3z = 5
5y + 6z = 5
Step Two
Add the second and third together.
- 2x - y + z = -3
2x + 3y + 3z = 5
2y + 4z = 2 Divide this result by 2
y + 2z = 1 multiply this result by 5
5y + 10z = 5
Step three
Subtract the result of step 2 from the result of step one
5y + 10z = 5
5y + 6z = 5 Subtract
4z = 0
z = 0
Step Four
Solve for y
5y + 6z = 5 But z = 0
5y = 5
y = 1
Step Four
Solve for x . Use equation 3 in the givens.
2x + 3y + 3z = 5
2x + 3*1) + 3*0 = 5
2x = 5 - 3
2x = 2
x = 1
Answer
x = 1
y = 1
z =0 This has been checked and found to be correct.
Problem 2
Substitution is not the best way to do this. Divide the last equation by 2 and add it to the first one.
Step One
divide equation 3 by 2.
x + z = 2
Step Two
Add step one to equation 1
-x - y - z = - 8
x + z = 2
- y = - 6
y = 6
Step Three
Put this result into equation 1.
-x - 6 - z = - 8
-x - z = - 2
x + z = 2 Multiply this equation by 4
4x + 4z = 8
Step four
Put y = 7 into the second equation.
-4x + 4y + 5z = 7
-4x + 4*6 + 5z = 7
-4x + 24 + 5z = 7
-4x +5z = -17
Step 5
Add the results from Step 3 and Step 4 together.
-4x + 5z = - 17
4x + 4z = 8
9z = - 9
z = - 1
Step 6
Find x
-x - y - z = - 8
-x -6 + 1 =- 8
-x - 5 = - 8
-x = - 3
x = 3
Answers
x = 3
y = 6
z = -1 verified to be correct.