Ask a New Question
Menu

Select all that are true about the system.

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.

1 answer

To determine which statements are true about the given system of equations, we need to check if the specified points satisfy the equations of both lines.

1. Line Equations:

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

Check each point:

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

  • For Line 1:
    \( 6(-6) - 7(1) = -36 - 7 = -43 \) (not equal to 26)
    Not a solution for Line 1.

  • For Line 2:
    \( 2(-6) + 9(1) = -12 + 9 = -3 \) (equal to -3)
    Is a solution for Line 2.

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

  • For Line 1:
    \( 6(3) - 7(-1) = 18 + 7 = 25 \) (not equal to 26)
    Not a solution for Line 1.

  • For Line 2:
    \( 2(3) + 9(-1) = 6 - 9 = -3 \) (equal to -3)
    Is a solution for Line 2.

Point \((0, 3)\):

  • For Line 1:
    \( 6(0) - 7(3) = 0 - 21 = -21 \) (not equal to 26)
    Not a solution for Line 1.

  • For Line 2:
    \( 2(0) + 9(3) = 0 + 27 = 27 \) (not equal to -3)
    Not a solution for Line 2.

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

  • For Line 1:
    \( 6(-3) - 7(1) = -18 - 7 = -25 \) (not equal to 26)
    Not a solution for Line 1.

  • For Line 2:
    \( 2(-3) + 9(1) = -6 + 9 = 3 \) (not equal to -3)
    Not a solution for Line 2.

Summary of Findings:

  1. \((-6, 1)\) is a solution for Line 2 only. True.
  2. \((3, -1)\) is a solution to the system. False.
  3. \((0, 3)\) is a solution for Line 1 only. False.
  4. \((-3, 1)\) is a solution to the system. False.

Conclusion:

The only true statement is:

  • \((-6, 1)\) is a solution for Line 2 only.