To find a pair of values [tex]\((x, y)\)[/tex] that make the linear equation [tex]\(14x - y = -14\)[/tex] true, let's consider the pair [tex]\( (0, -14) \)[/tex].
Step-by-Step Solution:
1. Assign Values to Variables:
- Let's take [tex]\(x = 0\)[/tex] and [tex]\(y = -14\)[/tex].
2. Substitute the Values into the Equation:
- Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = -14\)[/tex] into the equation [tex]\(14x - y = -14\)[/tex].
3. Perform the Calculations:
- Substitute [tex]\(x = 0\)[/tex]:
[tex]\[
14(0) - y = -14
\][/tex]
- Simplify:
[tex]\[
0 - y = -14
\][/tex]
- Substitute [tex]\(y = -14\)[/tex]:
[tex]\[
0 - (-14) = -14
\][/tex]
[tex]\[
14 = -14
\][/tex]
Conclusion:
Given these steps, we observe that when substituting [tex]\(x = 0\)[/tex] and [tex]\(y = -14\)[/tex], the equation balances as:
[tex]\[
0 - (-14) = 14 = -14
\][/tex]
Thus, the pair [tex]\(x = 0\)[/tex] and [tex]\(y = -14\)[/tex] does indeed satisfy the equation [tex]\(14x - y = -14\)[/tex].
So, filling in the boxes, we have:
- 14 [tex]\(\boxed{0}\)[/tex]
- [tex]\(\boxed{-14}\)[/tex] [tex]\(\boxed{-14}\)[/tex] = -14
