Answer:
156 and 23
Step-by-step explanation:
- We can use system of equations to solve this problem.
Step 1: Set up the system of equations.
- [tex]\left \{ {{x+y=179} \atop {x-y=133}} \right.[/tex]
Step 2: Solve x + y = 179 for x.
- [tex]x + y = 179[/tex]
- [tex]x + y - y = 179 - y[/tex] (Subtract y from both sides)
- [tex]x = -y + 179[/tex]
Step 3: Substitute -y + 179 for x in x - y = 133.
- [tex]x-y=133[/tex]
- [tex]-y+179-y=133[/tex]
- [tex](-y-y)+(179)=133[/tex] (Combine like terms)
- [tex]-2y + 179 = 133[/tex]
- [tex]-2y + 179 - 179 = 133 - 179[/tex] (Subtract 179 from both sides)
- [tex]-2y = -46[/tex]
- [tex]\frac{-2y}{-2} = \frac{-46}{-2}[/tex] (Divide both sides by -2)
- [tex]y = 23[/tex]
Step 4: Substitute 23 for y in x = -y + 179
- [tex]x = -23 + 179[/tex]
- [tex]x = 156[/tex]
Therefore, the numbers are 156 and 23.
