Question 15907: how do you solve this problem using substitution?
X + Y-Z=3
-3X +Z=-5
X +2Y-Z=3
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website!
` X +` Y - Z =` 3
-3X ` ` `+ Z = -5
` X + 2Y - Z =` 3
`
Here are the seven steps.
1. Pick a letter. (If one of the equations has only two letters, choose the
` `letter that is missing)
2. Pick an equation that contains that letter
3. Solve for that letter in that equation.
4. Substitute what you get into any other equations that contains that letter,
` `and simplify.
5. Now you have only two equations in one unknown
6. Solve that system for the two letters they contain
7. Substitute the values of those two letters in the result of step 3.
`
1. Pick a letter. (If one of the equations has only two letters, choose the
letter that is missing)
`
Since the second equation, -3X +Z=-5, has no Y, we pick Y
`
2. Pick an equation that contains that letter
`
I pick the first equation
X + Y - Z = 3
`
3. Solve for that letter in that equation.
`
X + Y - Z = 3
` ` ` ` Y = 3 - X + Z
`
4. Substitute what you get into any other equations that contains
` `that letter, and simplify.
`
The third equation, X + 2Y - Z = 3, contains Y, so replace Y by 3-X+Z
in it and simplify
`
` ` ` ` ` X + 2Y - Z = 3
X + 2(3 - X + Z) - Z = 3
`X + 6 - 2X + 2Z - Z = 3
` ` ` ` ` ` ` -X + Z = -3
`
5. Now you have only two equations in one unknown
`
These are
`
-3X + Z = -5 and -X + Z = -3
`
6. Solve that system for the two letters they contain.
`
-3X + Z = -5
`-X + Z = -3
`
Solve for Z in the second one just above,
`
` ` ` Z = -3 + X
`
Substitute -3+X for Z in the first one just above
`
` ` ` `-3X + Z = -5
-3X + (-3 + X) = -5
` `-3X - 3 + X = -5
` ` ` ` ` `-2X = -2
` ` ` ` ` ` `X = 1
`
Substitute 1 for X in Z = -3 + X
`
Z = -3 + (1) = -3 + 1 = -2
`
7. Substitute the values of those two letters in the result of step 3.
`
Substitute 1 for X and -5 for Z in Y = 3 - X + Z
`
Y = 3 - X + Z
Y = 3 - (1) + (-2)
Y = 3 - 1 - 2
Y = 0
`
Edwin
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