Question
Solve the system of two equations using substitution.
y = 2 + 3x
1x - 3y = -16 (1 point)
• (2, 8)
• (-2, - 4)
• (-2, 4)
• (2, 10)
y = 2 + 3x
1x - 3y = -16 (1 point)
• (2, 8)
• (-2, - 4)
• (-2, 4)
• (2, 10)
Answers
GPT-4o mini
To solve the system of equations using substitution, we first have the equations:
1. \( y = 2 + 3x \)
2. \( x - 3y = -16 \)
Now, we'll substitute the expression for \( y \) from the first equation into the second equation.
Substituting for \( y \):
\[
x - 3(2 + 3x) = -16
\]
Now, simplify this equation:
\[
x - 6 - 9x = -16
\]
Combine like terms:
\[
-8x - 6 = -16
\]
Now, add 6 to both sides:
\[
-8x = -10
\]
Now divide by -8:
\[
x = \frac{10}{8} = \frac{5}{4}
\]
Next, we substitute \( x = \frac{5}{4} \) back into the first equation to find \( y \):
\[
y = 2 + 3\left(\frac{5}{4}\right)
\]
Calculating \( y \):
\[
y = 2 + \frac{15}{4} = \frac{8}{4} + \frac{15}{4} = \frac{23}{4}
\]
So the solution is:
\[
\left( \frac{5}{4}, \frac{23}{4} \right)
\]
This solution \( \left( \frac{5}{4}, \frac{23}{4} \right) \) does not match any of the provided answer choices. It seems that there might have been an error in interpreting the equations as represented in the list of potential answers. Let's check them:
We'll double-check if the equations can yield any integer solutions from the provided options.
### Check the provided options:
1. **Option (2, 8)**:
- For \( x = 2 \):
\[
y = 2 + 3(2) = 8
\]
- Check second equation:
\[
2 - 3(8) = 2 - 24 = -22 \quad \text{(not a solution)}
\]
2. **Option (-2, -4)**:
- For \( x = -2 \):
\[
y = 2 + 3(-2) = 2 - 6 = -4
\]
- Check second equation:
\[
-2 - 3(-4) = -2 + 12 = 10 \quad \text{(not a solution)}
\]
3. **Option (-2, 4)**:
- For \( x = -2 \):
\[
y = 2 + 3(-2) = 2 - 6 = -4 \quad \text{(not a solution as y is not 4)}
\]
4. **Option (2, 10)**:
- For \( x = 2 \):
\[
y = 2 + 3(2) = 2 + 6 = 8 \quad \text{(not a solution as y is not 10)}
\]
None of the options seem to be correct based on the original substitution approach.
If you'd like any further exploration or action on this system, please clarify, but it seems there are no corresponding integer solutions amongst the presented choices.
1. \( y = 2 + 3x \)
2. \( x - 3y = -16 \)
Now, we'll substitute the expression for \( y \) from the first equation into the second equation.
Substituting for \( y \):
\[
x - 3(2 + 3x) = -16
\]
Now, simplify this equation:
\[
x - 6 - 9x = -16
\]
Combine like terms:
\[
-8x - 6 = -16
\]
Now, add 6 to both sides:
\[
-8x = -10
\]
Now divide by -8:
\[
x = \frac{10}{8} = \frac{5}{4}
\]
Next, we substitute \( x = \frac{5}{4} \) back into the first equation to find \( y \):
\[
y = 2 + 3\left(\frac{5}{4}\right)
\]
Calculating \( y \):
\[
y = 2 + \frac{15}{4} = \frac{8}{4} + \frac{15}{4} = \frac{23}{4}
\]
So the solution is:
\[
\left( \frac{5}{4}, \frac{23}{4} \right)
\]
This solution \( \left( \frac{5}{4}, \frac{23}{4} \right) \) does not match any of the provided answer choices. It seems that there might have been an error in interpreting the equations as represented in the list of potential answers. Let's check them:
We'll double-check if the equations can yield any integer solutions from the provided options.
### Check the provided options:
1. **Option (2, 8)**:
- For \( x = 2 \):
\[
y = 2 + 3(2) = 8
\]
- Check second equation:
\[
2 - 3(8) = 2 - 24 = -22 \quad \text{(not a solution)}
\]
2. **Option (-2, -4)**:
- For \( x = -2 \):
\[
y = 2 + 3(-2) = 2 - 6 = -4
\]
- Check second equation:
\[
-2 - 3(-4) = -2 + 12 = 10 \quad \text{(not a solution)}
\]
3. **Option (-2, 4)**:
- For \( x = -2 \):
\[
y = 2 + 3(-2) = 2 - 6 = -4 \quad \text{(not a solution as y is not 4)}
\]
4. **Option (2, 10)**:
- For \( x = 2 \):
\[
y = 2 + 3(2) = 2 + 6 = 8 \quad \text{(not a solution as y is not 10)}
\]
None of the options seem to be correct based on the original substitution approach.
If you'd like any further exploration or action on this system, please clarify, but it seems there are no corresponding integer solutions amongst the presented choices.