`ifx[{:(2),(3):}]+y[{:(-1),(1):}]=[{:(10),(5):}],`find the values of x and y.

Explanation

To solve the equation \( x \begin{pmatrix} 2 & 3 \end{pmatrix} + y \begin{pmatrix} -1 & 1 \end{pmatrix} = \begin{pmatrix} 10 & 5 \end{pmatrix} \), we will follow these steps:

### Step 1: Write the equation in expanded form
We start by expanding the left-hand side of the equation:

\[ x \begin{pmatrix} 2 & 3 \end{pmatrix} + y \begin{pmatrix} -1 & 1 \end{pmatrix} = \begin{pmatrix} 2x & 3x \end{pmatrix} + \begin{pmatrix} -y & y \end{pmatrix} \]

### Step 2: Combine the matrices
Now we combine the matrices:

\[ \begin{pmatrix} 2x - y & 3x + y \end{pmatrix} = \begin{pmatrix} 10 & 5 \end{pmatrix} \]

### Step 3: Set up equations
From the equality of the matrices, we can set up two separate equations:

1. \( 2x - y = 10 \) (Equation 1)
2. \( 3x + y = 5 \) (Equation 2)

### Step 4: Solve the equations
Now, we will solve these equations simultaneously. We can start by adding the two equations to eliminate \(y\):

\[ (2x - y) + (3x + y) = 10 + 5 \]

This simplifies to:

\[ 5x = 15 \]

### Step 5: Solve for \(x\)
Now, divide both sides by 5:

\[ x = 3 \]

### Step 6: Substitute \(x\) back into one of the equations
We will substitute \(x = 3\) back into Equation 1 to find \(y\):

\[ 2(3) - y = 10 \]

This simplifies to:

\[ 6 - y = 10 \]

### Step 7: Solve for \(y\)
Now, rearranging gives:

\[ -y = 10 - 6 \]
\[ -y = 4 \]

Thus, multiplying both sides by -1 gives:

\[ y = -4 \]

### Final Answer
The values of \(x\) and \(y\) are:

\[ x = 3, \quad y = -4 \]

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