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Which of these systems of equations have a solution of (6, -2)? Select all that apply.2x+5y=2–2x+3y=–18y=–x+4y=–13xy=23x–63x+10y=–2y=x+8y=2x–14y=12x–5x–y=4x+2y=2x–3y=12Submit

Question

Which of these systems of equations have a solution of (6, -2)? Select all that apply.2x+5y=2–2x+3y=–18y=–x+4y=–13xy=23x–63x+10y=–2y=x+8y=2x–14y=12x–5x–y=4x+2y=2x–3y=12Submit

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Solution

To find out which of these systems of equations have a solution of (6, -2), we need to substitute x=6 and y=-2 into each equation and see if both sides of the equation are equal.

  1. For the equation 2x+5y=2, substituting x=6 and y=-2 gives 26 + 5(-2) = 12 - 10 = 2, which is true. So, this equation has a solution of (6, -2).

  2. For the equation -2x+3y=-18, substituting x=6 and y=-2 gives -26 + 3(-2) = -12 - 6 = -18, which is true. So, this equation also has a solution of (6, -2).

  3. For the equation y=-x+4, substituting x=6 and y=-2 gives -2 = -6 + 4 = -2, which is true. So, this equation also has a solution of (6, -2).

  4. For the equation y=-13x, substituting x=6 and y=-2 gives -2 = -13*6 = -78, which is false. So, this equation does not have a solution of (6, -2).

  5. For the equation y=23x-63, substituting x=6 and y=-2 gives -2 = 23*6 - 63 = 69, which is false. So, this equation does not have a solution of (6, -2).

  6. For the equation 3x+10y=-2, substituting x=6 and y=-2 gives 36 + 10(-2) = 18 - 20 = -2, which is true. So, this equation also has a solution of (6, -2).

  7. For the equation y=x+8, substituting x=6 and y=-2 gives -2 = 6 + 8 = 14, which is false. So, this equation does not have a solution of (6, -2).

  8. For the equation y=2x-14, substituting x=6 and y=-2 gives -2 = 2*6 - 14 = -2, which is true. So, this equation also has a solution of (6, -2).

  9. For the equation y=12x-5, substituting x=6 and y=-2 gives -2 = 12*6 - 5 = 67, which is false. So, this equation does not have a solution of (6, -2).

  10. For the equation x-y=4, substituting x=6 and y=-2 gives 6 - (-2) = 8, which is false. So, this equation does not have a solution of (6, -2).

  11. For the equation x+2y=2, substituting x=6 and y=-2 gives 6 + 2*(-2) = 2, which is true. So, this equation also has a solution of (6, -2).

  12. For the equation x-3y=12, substituting x=6 and y=-2 gives 6 - 3*(-2) = 12, which is true. So, this equation also has a solution of (6, -2).

So, the systems of equations that have a solution of (6, -2) are: 2x+5y=2, -2x+3y=-18, y=-x+4, 3x+10y=-2, y=2x-14, x+2y=2, and x-3y=12.

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