Answer:
The first integer is: -49
The second integer: -49+1 = -48
Solution Check:
-49+(-48) = -97
Explanation:
Let the first integer:
![x](https://img.qammunity.org/2021/formulas/mathematics/middle-school/p9sq9b3rc5nwoqzhzc8wcaj51b36281l9g.png)
As we are looking for a consecutive integer, so
The second integer would be:
![x+1](https://img.qammunity.org/2021/formulas/mathematics/middle-school/sc05fc0ptmxj3vzw3r1ed0jp33ct3crkp0.png)
We know the sum of these two integers is -97. Thus, we can write this equation and solve for 'x'.
![x+\left(x+1\right)=-97](https://img.qammunity.org/2021/formulas/mathematics/high-school/kaxzw4zdgj9rjs2qos4iq2yjdqx7ebxcvr.png)
![x+x+1=-97](https://img.qammunity.org/2021/formulas/mathematics/high-school/ebmvx6cd2jg5anfykr3k9jc9txa7xld8td.png)
![2x+1=-97](https://img.qammunity.org/2021/formulas/mathematics/high-school/efs7hrfj7y8kcsyqgkbgqsdps1hf44lke9.png)
![2x=-98](https://img.qammunity.org/2021/formulas/mathematics/high-school/jnlqgot85farejabbys66qubr55c67qtv0.png)
Divide both sides by 2
![(2x)/(2)=(-98)/(2)](https://img.qammunity.org/2021/formulas/mathematics/high-school/y8o2tdi04o11p7z0dy8ju75vn0r87u58iz.png)
![x=-49](https://img.qammunity.org/2021/formulas/mathematics/high-school/3zxm63trvssnr3wp1uhb71xhqeh9d8ou77.png)
Therefore,
The first integer is: -49
The second integer: -49+1 = -48
Solution Check:
-49+(-48) = -97