58 and 39
To solve
Create a system of equations.
Say one number is X and the other is Y.
X+Y=97
X-Y=19
Use the first equation to find the value of either X or Y. I’m going to find it in terms of Y.
Subtract X from both sides.
X+Y=97 —> Y=97-X
Now, use that Y value and replace it in the second equation.
X-Y=19 —> X-(97-X)=19
Now solve for X.
1. Distribute terms in the parenthesis
X-97+X=19
2. Combine like terms.
2X-97=19
3. Add 97 to both sides
2X=116
4. Divide both sides by 2
X=58
Now, we can plug the X value in to any of the two first equations to solve for Y.
X+Y=97
58+Y=97
Subtract 58 from both sides and you get Y=39
X=58 and Y=39