Sure, let's solve each of these four equations step-by-step with [tex]\( x = -3 \)[/tex].
1. First Equation: [tex]\( y = 2x + 5 \)[/tex]
- Substitute [tex]\( x = -3 \)[/tex]:
[tex]\[
y = 2(-3) + 5
\][/tex]
- Compute the multiplication:
[tex]\[
y = -6 + 5
\][/tex]
- Compute the addition:
[tex]\[
y = -1
\][/tex]
Therefore, for the first equation, [tex]\( y = -1 \)[/tex].
2. Second Equation: [tex]\( y = x^2 - 4 \)[/tex]
- Substitute [tex]\( x = -3 \)[/tex]:
[tex]\[
y = (-3)^2 - 4
\][/tex]
- Compute the square:
[tex]\[
y = 9 - 4
\][/tex]
- Compute the subtraction:
[tex]\[
y = 5
\][/tex]
Therefore, for the second equation, [tex]\( y = 5 \)[/tex].
3. Third Equation: [tex]\( y = 3x - 7 \)[/tex]
- Substitute [tex]\( x = -3 \)[/tex]:
[tex]\[
y = 3(-3) - 7
\][/tex]
- Compute the multiplication:
[tex]\[
y = -9 - 7
\][/tex]
- Compute the subtraction:
[tex]\[
y = -16
\][/tex]
Therefore, for the third equation, [tex]\( y = -16 \)[/tex].
4. Fourth Equation: [tex]\( y = \frac{1}{x + 2} \)[/tex]
- Substitute [tex]\( x = -3 \)[/tex]:
[tex]\[
y = \frac{1}{-3 + 2}
\][/tex]
- Compute the addition:
[tex]\[
y = \frac{1}{-1}
\][/tex]
- Compute the division:
[tex]\[
y = -1
\][/tex]
Therefore, for the fourth equation, [tex]\( y = -1 \)[/tex].
To summarize the results for [tex]\( x = -3 \)[/tex]:
1. For the first equation [tex]\( y = 2x + 5 \)[/tex], [tex]\( y = -1 \)[/tex].
2. For the second equation [tex]\( y = x^2 - 4 \)[/tex], [tex]\( y = 5 \)[/tex].
3. For the third equation [tex]\( y = 3x - 7 \)[/tex], [tex]\( y = -16 \)[/tex].
4. For the fourth equation [tex]\( y = \frac{1}{x + 2} \)[/tex], [tex]\( y = -1 \)[/tex].
So the final results are [tex]\((-1, 5, -16, -1)\)[/tex].
