If `(2x+y,7)=(5,y-3)` then find `x` and `y`

Explanation

To solve the equation \( (2x + y, 7) = (5, y - 3) \), we can break it down into two separate equations based on the equality of the ordered pairs.

### Step 1: Set up the equations
From the given ordered pairs, we can equate the first components and the second components:
1. \( 2x + y = 5 \) (Equation 1)
2. \( 7 = y - 3 \) (Equation 2)

### Step 2: Solve Equation 2 for \( y \)
From Equation 2, we can isolate \( y \):
\[ y - 3 = 7 \]
Adding 3 to both sides gives:
\[ y = 7 + 3 \]
\[ y = 10 \]

### Step 3: Substitute \( y \) into Equation 1
Now that we have the value of \( y \), we can substitute it back into Equation 1:
\[ 2x + y = 5 \]
Substituting \( y = 10 \):
\[ 2x + 10 = 5 \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \):
\[ 2x + 10 = 5 \]
Subtracting 10 from both sides:
\[ 2x = 5 - 10 \]
\[ 2x = -5 \]
Dividing both sides by 2:
\[ x = -\frac{5}{2} \]

### Final Answer
Thus, the values of \( x \) and \( y \) are:
\[ x = -\frac{5}{2}, \quad y = 10 \]

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