To find the two numbers given their sum and difference, let's use a step-by-step approach:
1. Define the variables:
- Let the two numbers be [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
2. Setup the equations:
- The sum of the two numbers is given as 54:
[tex]\[
x + y = 54
\][/tex]
- The difference of the two numbers is given as 86:
[tex]\[
x - y = 86
\][/tex]
3. Add the two equations to eliminate [tex]\( y \)[/tex]:
[tex]\[
(x + y) + (x - y) = 54 + 86
\][/tex]
Simplifying the left side:
[tex]\[
x + y + x - y = 54 + 86
\][/tex]
[tex]\[
2x = 140
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{140}{2}
\][/tex]
[tex]\[
x = 70
\][/tex]
5. Substitute [tex]\( x \)[/tex] back into the equation [tex]\( x + y = 54 \)[/tex] to find [tex]\( y \)[/tex]:
[tex]\[
70 + y = 54
\][/tex]
Subtract 70 from both sides to isolate [tex]\( y \)[/tex]:
[tex]\[
y = 54 - 70
\][/tex]
[tex]\[
y = -16
\][/tex]
6. Conclusion:
- The two numbers are [tex]\( 70 \)[/tex] and [tex]\( -16 \)[/tex].
Therefore, the two numbers are 70 and -16.
