Questions: y=x+8 x+y=2

Transcript text: $\begin{array}{l}y=x+8 \\ x+y=2\end{array}$

Solution

Solution Steps

To solve the system of equations, we can use substitution or elimination. Here, we will use substitution. First, solve the first equation for $ y $ in terms of $ x $. Then, substitute this expression for $ y $ into the second equation to find the value of $ x $. Finally, substitute the value of $ x $ back into the first equation to find the value of $ y $.

Step 1: Solve for $ y $

From the first equation $ y = x + 8 $, we can express $ y $ in terms of $ x $.

Step 2: Substitute into the second equation

Substituting $ y $ into the second equation $ x + y = 2 $ gives us: \[ x + (x + 8) = 2 \] This simplifies to: \[ 2x + 8 = 2 \]

Step 3: Solve for $ x $

Rearranging the equation $ 2x + 8 = 2 $ leads to: \[ 2x = 2 - 8 \] \[ 2x = -6 \] Dividing both sides by 2, we find: \[ x = -3 \]

Step 4: Solve for $ y $

Now, substituting $ x = -3 $ back into the equation $ y = x + 8 $: \[ y = -3 + 8 = 5 \]

Final Answer

The solution to the system of equations is: \[ \boxed{x = -3} \] \[ \boxed{y = 5} \]

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