If 4x + 5y = -5 is a true equation, what would be the value of 8 + 4x + 5y?
Understand the Problem
The question is asking us to find the value of the expression 8 + 4x + 5y given that the equation 4x + 5y = -5 is true. To solve it, we will first substitute -5 for 4x + 5y in the expression.
Answer
The value of \( 8 + 4x + 5y \) is \( 3 \).
Answer for screen readers
The value of ( 8 + 4x + 5y ) is ( 3 ).
Steps to Solve
- Substituting the given equation
We know from the problem that ( 4x + 5y = -5 ). We will substitute this value into the expression ( 8 + 4x + 5y ).
- Replacing ( 4x + 5y )
This gives us the expression: $$ 8 + 4x + 5y = 8 + (-5) $$
- Simplifying the expression
Next, we simplify the expression: $$ 8 - 5 = 3 $$
The value of ( 8 + 4x + 5y ) is ( 3 ).
More Information
The calculation was straightforward due to the substitution of the known value from the equation. This type of substitution is a common technique in algebra.
Tips
- Students may forget to substitute the entire expression ( 4x + 5y ) with (-5), leading to incorrect interpretations of the problem.
- Failing to simplify the resulting arithmetic correctly can also lead to errors.
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