which of these systems of equations have a solution of (-12, 10)? select all that apply.
$y = -x - 2$
$-2x - y = 14$
$y = -3x - 26$
$y = 2x + 34$
$x = 12$
$x + y = -2$
$5x + 5y = -10$
$x - y = -22$
$3x + 4y = -4$
$y = -4x - 36$
$y = -5x - 50$
$y = 10$

Question

Accepted Answer

To determine which systems of equations have a solution of $(-12, 10)$, we substitute $x = -12$ and $y = 10$ into each equation of the system and check if both equations are satisfied.

### System 1: $y = -x - 2$ and $-2x - y = 14$
- For $y = -x - 2$:
  Substitute $x = -12$ and $y = 10$:
  $10 = -(-12) - 2 = 12 - 2 = 10$. This is true.
- For $-2x - y = 14$:
  Substitute $x = -12$ and $y = 10$:
  $-2(-12) - 10 = 24 - 10 = 14$. This is true.
So, this system has a solution of $(-12, 10)$.

### System 2: $y = -3x - 26$ and $y = 2x + 34$
- For $y = -3x - 26$:
  Substitute $x = -12$ and $y = 10$:
  $10 = -3(-12) - 26 = 36 - 26 = 10$. This is true.
- For $y = 2x + 34$:
  Substitute $x = -12$ and $y = 10$:
  $10 = 2(-12) + 34 = -24 + 34 = 10$. This is true.
So, this system has a solution of $(-12, 10)$.

### System 3: $x = 12$ and $x + y = -2$
- For $x = 12$:
  The given $x$ in the solution is $-12$, not $12$. So, this equation is false.
Thus, this system does not have a solution of $(-12, 10)$.

### System 4: $5x + 5y = -10$ and $x - y = -22$
- For $5x + 5y = -10$:
  Substitute $x = -12$ and $y = 10$:
  $5(-12) + 5(10) = -60 + 50 = -10$. This is true.
- For $x - y = -22$:
  Substitute $x = -12$ and $y = 10$:
  $-12 - 10 = -22$. This is true.
So, this system has a solution of $(-12, 10)$.

### System 5: $3x + 4y = -4$ and $y = -4x - 36$
- For $3x + 4y = -4$:
  Substitute $x = -12$ and $y = 10$:
  $3(-12) + 4(10) = -36 + 40 = 4
eq -4$. This is false.
Thus, this system does not have a solution of $(-12, 10)$.

### System 6: $y = -5x - 50$ and $y = 10$
- For $y = -5x - 50$:
  Substitute $x = -12$ and $y = 10$:
  $10 = -5(-12) - 50 = 60 - 50 = 10$. This is true.
- For $y = 10$:
  The given $y$ in the solution is $10$, so this is true.
So, this system has a solution of $(-12, 10)$.

### Final Answer
The systems of equations that have a solution of $(-12, 10)$ are:
- $y = -x - 2$ and $-2x - y = 14$
- $y = -3x - 26$ and $y = 2x + 34$
- $5x + 5y = -10$ and $x - y = -22$
- $y = -5x - 50$ and $y = 10$

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QUESTION IMAGE

Question

Explanation:

System 1: \(y = -x - 2\) and \(-2x - y = 14\)

System 2: \(y = -3x - 26\) and \(y = 2x + 34\)

System 3: \(x = 12\) and \(x + y = -2\)

System 4: \(5x + 5y = -10\) and \(x - y = -22\)

System 5: \(3x + 4y = -4\) and \(y = -4x - 36\)

System 6: \(y = -5x - 50\) and \(y = 10\)

Final Answer

Answer: