Which ordered pair is a solution for the system of equations?

Question

{3x−5y=152x−y=−4

Responses

(−5, −6)
begin ordered pair negative 5 comma negative 6 end ordered pair

(2, 8)
begin ordered pair 2 comma 8 end ordered pair

(0, 3)
begin ordered pair 0 comma 3 end ordered pair

(−6, −11)

Answer 1

To determine which of the provided ordered pairs are solutions to the system of equations given by:

1. \( 3x - 5y = 15 \)
2. \( 2x - y = -4 \)

we can substitute each ordered pair into both equations and check for validity.

Checking each ordered pair:

1. For the ordered pair \((-5, -6)\):

   • Substitute \(x = -5\) and \(y = -6\) into both equations. \[ 3(-5) - 5(-6) = -15 + 30 = 15 \quad \text{(First equation is satisfied)} \] \[ 2(-5) - (-6) = -10 + 6 = -4 \quad \text{(Second equation is satisfied)} \] Result: This pair is a solution.

2. For the ordered pair \((2, 8)\):

   • Substitute \(x = 2\) and \(y = 8\): \[ 3(2) - 5(8) = 6 - 40 = -34 \quad \text{(Not satisfied)} \] Result: This pair is NOT a solution.

3. For the ordered pair \((0, 3)\):

   • Substitute \(x = 0\) and \(y = 3\): \[ 3(0) - 5(3) = -15 \quad \text{(Not satisfied)} \] Result: This pair is NOT a solution.

4. For the ordered pair \((-6, -11)\):

   • Substitute \(x = -6\) and \(y = -11\): \[ 3(-6) - 5(-11) = -18 + 55 = 37 \quad \text{(Not satisfied)} \] Result: This pair is NOT a solution.

Conclusion:

The only ordered pair that is a solution to the system of equations is \((-5, -6)\).