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

Explanation

To solve the equation \((2x+y, 7) = (5, y-3)\), we will equate the corresponding components of the ordered pairs.

### Step 1: Set up the equations
From the given equation, we can separate it into two equations:
1. \(2x + y = 5\) (from the first components)
2. \(7 = y - 3\) (from the second components)

### Step 2: Solve the second equation for \(y\)
From the second equation \(7 = y - 3\), we can solve for \(y\):
\[ y - 3 = 7 \]
Adding 3 to both sides gives:
\[ y = 10 \]

### Step 3: Substitute \(y\) into the first equation
Now that we have \(y = 10\), we can substitute this value into the first equation \(2x + y = 5\):
\[ 2x + 10 = 5 \]

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

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