Question

Select all that are true about the system.

systems of equation made up of lines 1 and 2
line 1 6x-7y=25
line 2 2x+9y=-3
Submit

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

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

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

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

Answer 1

To determine which statements are true, we will check each point against both equations of the lines given.

**Line 1: \(6x - 7y = 25\)**
**Line 2: \(2x + 9y = -3\)**

We will substitute each point into the equations to see if they satisfy the respective equations.

1. **For the point \((0, 3)\)**:
- For Line 1:
\(6(0) - 7(3) = 0 - 21 = -21 \neq 25\)
(Not a solution for Line 1)
- For Line 2:
\(2(0) + 9(3) = 0 + 27 = 27 \neq -3\)
(Not a solution for Line 2)

Conclusion: \((0, 3)\) is **not a solution for either line**.

2. **For the point \((3, -1)\)**:
- For Line 1:
\(6(3) - 7(-1) = 18 + 7 = 25\)
(Is a solution for Line 1)
- For Line 2:
\(2(3) + 9(-1) = 6 - 9 = -3\)
(Is a solution for Line 2)

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

3. **For the point \((-6, 1)\)**:
- For Line 1:
\(6(-6) - 7(1) = -36 - 7 = -43 \neq 25\)
(Not a solution for Line 1)
- For Line 2:
\(2(-6) + 9(1) = -12 + 9 = -3\)
(Is a solution for Line 2)

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

4. **For the point \((-3, 1)\)**:
- For Line 1:
\(6(-3) - 7(1) = -18 - 7 = -25 \neq 25\)
(Not a solution for Line 1)
- For Line 2:
\(2(-3) + 9(1) = -6 + 9 = 3 \neq -3\)
(Not a solution for Line 2)

Conclusion: \((-3, 1)\) is **not a solution for either line**.

### Final True Statements:
1. \((0, 3)\) is **not a solution for Line 1 only**.
2. \((3, -1)\) is **a solution to the system**.
3. \((-6, 1)\) is **a solution for Line 2 only**.
4. \((-3, 1)\) is **not a solution for the system or either line**.

So, the true statements are:
- \((3, -1)\) is a solution to the system.
- \((-6, 1)\) is a solution for Line 2 only.