Select all that are true about the system.

Question

Consdier the following system of equations made up of 1 and 2
line 1 :6x-7y=26
line 2; 2x+9y=-3

Submit

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

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

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

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

Answer 1

To determine which statements are true about the given system of equations, we should check each proposed point against both equations.

Equations:

1. \(6x - 7y = 26\) (Line 1)
2. \(2x + 9y = -3\) (Line 2)

Checking the points:

1. Point \((-6, 1)\):

   • Line 1: \(6(-6) - 7(1) = -36 - 7 = -43 \neq 26\) (not a solution)
   • Line 2: \(2(-6) + 9(1) = -12 + 9 = -3\) (a solution)
   • Conclusion: \((-6, 1)\) is a solution for Line 2 only. (True)

2. Point \((3, -1)\):

   • Line 1: \(6(3) - 7(-1) = 18 + 7 = 25 \neq 26\) (not a solution)
   • Line 2: \(2(3) + 9(-1) = 6 - 9 = -3\) (a solution)
   • Conclusion: \((3, -1)\) is not a solution to the system. (False)

3. Point \((0, 3)\):

   • Line 1: \(6(0) - 7(3) = 0 - 21 = -21 \neq 26\) (not a solution)
   • Line 2: \(2(0) + 9(3) = 0 + 27 = 27 \neq -3\) (not a solution)
   • Conclusion: \((0, 3)\) is not a solution for either line. (False)

4. Point \((-3, 1)\):

   • Line 1: \(6(-3) - 7(1) = -18 - 7 = -25 \neq 26\) (not a solution)
   • Line 2: \(2(-3) + 9(1) = -6 + 9 = 3 \neq -3\) (not a solution)
   • Conclusion: \((-3, 1)\) is not a solution for either line. (False)

Summary of the truth of the statements:

• \((-6, 1)\) is a solution for Line 2 only. (True)
• \((3, -1)\) is a solution to the system. (False)
• \((0, 3)\) is a solution for Line 1 only. (False)
• \((-3, 1)\) is a solution to the system. (False)

Thus, only the first statement is true.