Sure! Let's solve for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] in each of the given equations step-by-step:
### 1. Solving [tex]\(2x + y = -3\)[/tex]
1. Start with the equation:
[tex]\[
2x + y = -3
\][/tex]
2. Isolate [tex]\(y\)[/tex] by subtracting [tex]\(2x\)[/tex] from both sides:
[tex]\[
y = -2x - 3
\][/tex]
After solving, we get:
[tex]\[
y = -2x - 3
\][/tex]
### 2. Solving [tex]\(y = -2x - 3\)[/tex]
This equation is already solved for [tex]\(y\)[/tex]:
[tex]\[
y = -2x - 3
\][/tex]
### 3. Solving [tex]\(y = 2x - 3\)[/tex]
This equation is also already solved for [tex]\(y\)[/tex]:
[tex]\[
y = 2x - 3
\][/tex]
### 4. Solving [tex]\(-2x = -3 - y\)[/tex]
1. Start with the equation:
[tex]\[
-2x = -3 - y
\][/tex]
2. Add [tex]\(y\)[/tex] to both sides to move [tex]\(y\)[/tex] to the left side:
[tex]\[
-2x + y = -3
\][/tex]
3. Isolate [tex]\(y\)[/tex] by subtracting [tex]\(2x\)[/tex] from both sides:
[tex]\[
y = 2x - 3
\][/tex]
After solving, we get:
[tex]\[
y = 2x - 3
\][/tex]
Thus, the solutions for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] are:
[tex]\[
y = -2x - 3 \quad \text{(from the first and second equations)}
\][/tex]
[tex]\[
y = 2x - 3 \quad \text{(from the third and fourth equations)}
\][/tex]
