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For each ordered pair, determine whether it is a solution to the system of equations. { 7x-4y=6 -6x+7y=2 (x, y) Is it a solution? Yes or no?

(6,9) (-8,0) (3, 3) (-5,-4)

3 answers

To determine whether each ordered pair is a solution to the system of equations:

  1. \(7x - 4y = 6\)
  2. \(-6x + 7y = 2\)

we will substitute the values of \(x\) and \(y\) for each pair into both equations.

Check each pair:

  1. For (6, 9):

    • Substitute into the first equation: \[ 7(6) - 4(9) = 42 - 36 = 6 \quad \text{(True)} \]
    • Substitute into the second equation: \[ -6(6) + 7(9) = -36 + 63 = 27 \quad \text{(False)} \]
    • Is it a solution? No

  2. For (-8, 0):

    • Substitute into the first equation: \[ 7(-8) - 4(0) = -56 - 0 = -56 \quad \text{(False)} \]
    • Is it a solution? No

  3. For (3, 3):

    • Substitute into the first equation: \[ 7(3) - 4(3) = 21 - 12 = 9 \quad \text{(False)} \]
    • Is it a solution? No

  4. For (-5, -4):

    • Substitute into the first equation: \[ 7(-5) - 4(-4) = -35 + 16 = -19 \quad \text{(False)} \]
    • Is it a solution? No

Summary of results:

  • (6, 9): No
  • (-8, 0): No
  • (3, 3): No
  • (-5, -4): No

None of the ordered pairs are solutions to the system of equations.

bro aint no way none of them dont got an answer

Let's reevaluate each ordered pair to check if any of them is a solution to the system of equations properly.

The system of equations is:

  1. \( 7x - 4y = 6 \)
  2. \( -6x + 7y = 2 \)

We will substitute each pair \((x, y)\) and check.

Check each pair:

  1. For (6, 9):

    • Substitute into the first equation: \[ 7(6) - 4(9) = 42 - 36 = 6 \quad \text{(True)} \]
    • Substitute into the second equation: \[ -6(6) + 7(9) = -36 + 63 = 27 \quad \text{(False)} \]
    • Is it a solution? No

  2. For (-8, 0):

    • Substitute into the first equation: \[ 7(-8) - 4(0) = -56 - 0 = -56 \quad \text{(False)} \]
    • Is it a solution? No

  3. For (3, 3):

    • Substitute into the first equation: \[ 7(3) - 4(3) = 21 - 12 = 9 \quad \text{(False)} \]
    • Is it a solution? No

  4. For (-5, -4):

    • Substitute into the first equation: \[ 7(-5) - 4(-4) = -35 + 16 = -19 \quad \text{(False)} \]
    • Substitute into the second equation: \[ -6(-5) + 7(-4) = 30 - 28 = 2 \quad \text{(True)} \]
    • Is it a solution? No (it only works for the second equation)

Based on the checks, we confirm:

  • (6, 9): No
  • (-8, 0): No
  • (3, 3): No
  • (-5, -4): No

So, indeed, none of these pairs satisfy both equations simultaneously. If there’s a specific calculation you want me to explain or if you have other pairs, let me know!