Question

x | x - y = -5 | y
0 | (0) - y = -5 | 5
-6 | x - (-1) = -5 | -1
1 | 1 - y = -5 | 6
-5 | x - (0) = -5 | 0

Explanation:

Step1: Analyze the equation \(x - y = -5\)

We know the equation is \(x - y = -5\), which can be rewritten as \(y=x + 5\) or \(x=y - 5\). We will use the original form \(x - y=-5\) to find the missing values.

Step2: Find the missing \(y\) when \(x = 0\)

Substitute \(x = 0\) into \(x-y=-5\), we get \(0 - y=-5\), which simplifies to \(-y=-5\), so \(y = 5\).

Step3: Find the missing \(x\) when \(y=-1\)

Substitute \(y=-1\) into \(x - y=-5\), we have \(x-(-1)=-5\), which is \(x + 1=-5\), so \(x=-5 - 1=-6\).

Step4: Find the missing \(x\) when \(y = 4\)

Substitute \(y = 4\) into \(x - y=-5\), we get \(x-4=-5\), so \(x=-5 + 4=-1\) (Wait, there seems to be a typo in the original table, maybe the \(x\) value for \(y = 4\) should be calculated correctly. Wait, let's re - check. If \(y = 4\), then \(x-4=-5\), so \(x=-5 + 4=-1\), but in the table, the \(x\) value near \(y = 4\) is written as \(1\), maybe it's a mistake. But let's focus on the last row where \(y = 0\) and \(x=-5\). Substitute \(x=-5\) and \(y = 0\) into \(x - y=-5\), we have \(-5-0=-5\), which is correct. And for the last blank in the equation \(x-(\space)=-5\) when \(y = 0\), since \(x=-5\) and \(x - y=-5\), then \(y = 0\), so the blank should be \(0\)? Wait, no. Wait, the equation is \(x - y=-5\), when \(y = 0\), the equation is \(x-0=-5\), so the blank is \(0\). But let's go back to the original table's last row: \(x=-5\), \(y = 0\), so the equation is \(x-(0)=-5\), so the blank is \(0\).

Wait, maybe the main task is to fill the blanks. Let's re - organize:

1. When \(x = 0\), \(y\): From \(x - y=-5\), \(0-y=-5\Rightarrow y = 5\).
2. When \(y=-1\), \(x\): \(x-(-1)=-5\Rightarrow x + 1=-5\Rightarrow x=-6\).
3. When \(y = 4\), \(x\): \(x - 4=-5\Rightarrow x=-1\) (but the table has \(1\) there, maybe a mistake, but we follow the equation).
4. When \(x=-5\) and \(y = 0\), the equation is \(x-(0)=-5\), so the blank is \(0\).

Answer:

For the first blank (when \(x = 0\)), \(y = 5\); for the second blank (when \(y=-1\)), \(x=-6\); for the third blank (when \(y = 4\)), \(x=-1\); for the last blank (when \(x=-5,y = 0\)), the value in the parentheses is \(0\). (The final answers depend on which blank is being asked, but if we consider the last blank in \(x-(\space)=-5\) with \(x=-5,y = 0\), the answer is \(0\))