Math Problem Statement
a) Find the value of 4x − 6y when x = 3 and y = −2. b) Find the value of 2a^2 + 5b^2 when a = −6 and b = 2.
Solution
Let's solve the two parts of the question:
(a) Find the value of when and :
Substitute the values of and into the expression:
So, the value of is 24.
(b) Find the value of when and :
Substitute the values of and into the expression:
So, the value of is 92.
Would you like more details or have any questions on the steps?
Related Questions:
- What happens if the signs of and change in part (a)?
- How would you solve part (b) if both and were positive?
- Can you generalize the expression in part (a) for arbitrary values of and ?
- How does the solution to part (b) change if or is zero?
- What if you had to find the value of instead in part (a)?
Tip:
When squaring negative numbers, the result is always positive, as .
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Math Problem Analysis
Mathematical Concepts
Algebra
Substitution
Quadratic Expressions
Arithmetic Operations
Formulas
4x - 6y
2a^2 + 5b^2
Theorems
-
Suitable Grade Level
Grades 7-9