Question

Select all that are true about the system.

Consider the following system of equations made up of lines 1 and 2.
Line 1: 6x - 7y = 25
Line 2: 2x + 9y = -3
Select one or more answers!

Submit

(
0
,
3
)
(0,3)
is a solution for Line 1 only.

(
−
6
,
1
)
(−6,1)
is a solution for Line 2 only.

(
3
,
−
1
)
(3,−1)
is a solution to the system.

(
−
3
,
1
)
(−3,1)
is a solution to the system.

Answer 1

To determine which statements about the system of equations are true, we need to check each point against both equations.

**Line 1:** \( 6x - 7y = 25 \)

**Line 2:** \( 2x + 9y = -3 \)

We'll check each point one by one.

### Check point (0, 3):
**Line 1:**
\[ 6(0) - 7(3) = 0 - 21 = -21 \quad (\text{not a solution}) \]

**Line 2:**
\[ 2(0) + 9(3) = 0 + 27 = 27 \quad (\text{not a solution}) \]

**Conclusion:** (0, 3) is neither a solution for Line 1 nor Line 2.

### Check point (-6, 1):
**Line 1:**
\[ 6(-6) - 7(1) = -36 - 7 = -43 \quad (\text{not a solution}) \]

**Line 2:**
\[ 2(-6) + 9(1) = -12 + 9 = -3 \quad (\text{solution}) \]

**Conclusion:** (-6, 1) is a solution for Line 2 only.

### Check point (3, -1):
**Line 1:**
\[ 6(3) - 7(-1) = 18 + 7 = 25 \quad (\text{solution}) \]

**Line 2:**
\[ 2(3) + 9(-1) = 6 - 9 = -3 \quad (\text{solution}) \]

**Conclusion:** (3, -1) is a solution to the system.

### Check point (-3, 1):
**Line 1:**
\[ 6(-3) - 7(1) = -18 - 7 = -25 \quad (\text{not a solution}) \]

**Line 2:**
\[ 2(-3) + 9(1) = -6 + 9 = 3 \quad (\text{not a solution}) \]

**Conclusion:** (-3, 1) is neither a solution for Line 1 nor Line 2.

### Summary of the results:
1. (0, 3) is **not** a solution for Line 1 or Line 2.
2. (-6, 1) is a solution for Line 2 **only**.
3. (3, -1) is a solution to the system.
4. (-3, 1) is **not** a solution for Line 1 or Line 2.

### Selected Answers:
- **(−6, 1) is a solution for Line 2 only.**
- **(3, −1) is a solution to the system.**