https://file.aiquickdraw.com/mathbot/file/1727371081930ox9s3u8r.jpg

Let's solve the two parts of the question:

### (a) Find the value of \( 4x - 6y \) when \( x = 3 \) and \( y = -2 \):

Substitute the values of \( x \) and \( y \) into the expression:

\[
4(3) - 6(-2) = 12 + 12 = 24
\]

So, the value of \( 4x - 6y \) is **24**.

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### (b) Find the value of \( 2a^2 + 5b^2 \) when \( a = -6 \) and \( b = 2 \):

Substitute the values of \( a \) and \( b \) into the expression:

\[
2(-6)^2 + 5(2)^2 = 2(36) + 5(4) = 72 + 20 = 92
\]

So, the value of \( 2a^2 + 5b^2 \) is **92**.

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Would you like more details or have any questions on the steps?

### Related Questions:
1. What happens if the signs of \( x \) and \( y \) change in part (a)?
2. How would you solve part (b) if both \( a \) and \( b \) were positive?
3. Can you generalize the expression in part (a) for arbitrary values of \( x \) and \( y \)?
4. How does the solution to part (b) change if \( a \) or \( b \) is zero?
5. What if you had to find the value of \( 4x + 6y \) instead in part (a)?

### Tip:
When squaring negative numbers, the result is always positive, as \((-n)^2 = n^2\).

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.

Learn how to solve algebraic expressions using substitution. Find the value of 4x − 6y when x = 3 and y = −2, and calculate 2a^2 + 5b^2 for a = −6 and b = 2. Suitable for students in Grades 7-9.

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