Question

consider of the following system of equations made up of lines 1 and 2
line 1 6x - 7y = 25
line 2 2x+ 9y = -3
answers
a. (0,3/0 is a solution for only line 1
b. (-6,1) is a sulotions for line 2
c. (3, -1) is the solutions to the system.
d. (-3, 1)_is a solution to the system

Answer 1

To determine which of the provided statements about the system of equations is true, we can evaluate each proposed solution against both equations.

The system of equations is:

1. \( 6x - 7y = 25 \) (line 1)
2. \( 2x + 9y = -3 \) (line 2)

### Checking each option:

**a. \( (0, \frac{3}{0}) \)**
- Note: The expression \( \frac{3}{0} \) is undefined. So this option is not valid.

**b. \( (-6, 1) \)**
- Check line 2:
\[
2(-6) + 9(1) = -12 + 9 = -3
\]
This is correct, so **(-6, 1) is a solution for line 2**.

**c. \( (3, -1) \)**
- Check line 1:
\[
6(3) - 7(-1) = 18 + 7 = 25
\]
This holds true.
- Check line 2:
\[
2(3) + 9(-1) = 6 - 9 = -3
\]
This holds true as well, so **(3, -1) is a solution to the system**.

**d. \( (-3, 1) \)**
- Check line 1:
\[
6(-3) - 7(1) = -18 - 7 = -25
\]
This does not equal 25, so it is **not a solution for line 1**.

Conclusion:
- Option **a** is invalid due to the undefined value.
- Option **b** is a valid solution for line 2 only.
- Option **c** is a valid solution for both lines, hence a solution to the system.
- Option **d** is not a solution to the system.

**The correct answers are b and c, with c being a solution to the entire system.**