Question
se: \( \left\{\begin{array}{l}x+y=12 \\ x-y=4\end{array}\right. \)
Ask by Floyd Greene. in Angola
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A solução do sistema é \( x = 8 \) e \( y = 4 \).
Solution
Vamos resolver o sistema de equações:
x + y = 12 (1)
x – y = 4 (2)
Somando as equações (1) e (2):
(x + y) + (x – y) = 12 + 4
2x = 16
x = 16 / 2 = 8
Agora, substituindo o valor de x na equação (1):
8 + y = 12
y = 12 – 8 = 4
Portanto, a solução do sistema é:
x = 8
y = 4
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
To solve the system of equations, you can use the method of substitution or elimination. Let's use the elimination method here. First, add both equations: 1. \( x + y = 12 \) 2. \( x - y = 4 \) When you add them, the \(y\) cancels out: \[ (x + y) + (x - y) = 12 + 4 \implies 2x = 16 \implies x = 8. \] Now substitute \(x = 8\) back into one of the original equations to find \(y\): \[ 8 + y = 12 \implies y = 4. \] So, the solution is \(x = 8\) and \(y = 4\). Now you have found the solution to the system of equations! This kind of problem is common in algebra, so practicing more will help to cement your skills!
