If 3x - 2y + z = 15, what is 4x + y - z?
Understand the Problem
The question is presenting a mathematical expression that needs to be solved, likely requiring simplification or evaluation of the expression given.
Answer
The expression evaluates to \(7x - y - 15\).
Answer for screen readers
The value of (4x + y - z) is (7x - y - 15).
Steps to Solve
- Understanding the equations We have two expressions to work with:
- (3x - 2y + z = 15)
- We need to find the value of (4x + y - z).
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Expressing (z) in terms of (x) and (y) From the first equation, we can isolate (z): [ z = 15 - 3x + 2y ]
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Substituting (z) into the expression We substitute the expression for (z) into (4x + y - z): [ 4x + y - z = 4x + y - (15 - 3x + 2y) ]
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Simplifying the expression Now simplify (4x + y - (15 - 3x + 2y)): [ = 4x + y - 15 + 3x - 2y ] Combine like terms: [ = (4x + 3x) + (y - 2y) - 15 ] [ = 7x - y - 15 ]
The value of (4x + y - z) is (7x - y - 15).
More Information
This expression reveals the relationship between (x) and (y) based on the initial equation. If specific values for (x) and (y) are given, you can substitute them in to calculate a numerical result.
Tips
- Neglecting to distribute the negative sign when substituting for (z). Always remember that subtracting a term involves changing the signs.
- Forgetting to collect like terms in the simplification step.
