To solve the given questions, let’s analyze the function [tex]\( y = -2x + 3 \)[/tex] step-by-step.
### Part (a): Find [tex]\( y \)[/tex] when [tex]\( x = 3 \)[/tex]
1. Substitute [tex]\( x = 3 \)[/tex] into the equation [tex]\( y = -2x + 3 \)[/tex].
2. [tex]\( y = -2(3) + 3 \)[/tex]
3. Perform the multiplication inside the parenthesis: [tex]\( y = -6 + 3 \)[/tex]
4. Finally, perform the addition: [tex]\( y = -3 \)[/tex]
So, when [tex]\( x = 3 \)[/tex], [tex]\( y = -3 \)[/tex].
### Part (b): If [tex]\( y = 11 \)[/tex], find [tex]\( x \)[/tex]
1. Substitute [tex]\( y = 11 \)[/tex] into the equation [tex]\( y = -2x + 3 \)[/tex].
2. [tex]\( 11 = -2x + 3 \)[/tex]
3. To isolate [tex]\( x \)[/tex], first subtract 3 from both sides: [tex]\( 11 - 3 = -2x \)[/tex]
4. Simplify the left side: [tex]\( 8 = -2x \)[/tex]
5. To solve for [tex]\( x \)[/tex], divide both sides by -2: [tex]\( x = \frac{8}{-2} \)[/tex]
6. Simplify the division: [tex]\( x = -4 \)[/tex]
So, when [tex]\( y = 11 \)[/tex], [tex]\( x = -4 \)[/tex].
### Summary:
- When [tex]\( x = 3 \)[/tex], [tex]\( y = -3 \)[/tex].
- When [tex]\( y = 11 \)[/tex], [tex]\( x = -4 \)[/tex].
These are the solutions to the given problems.
