Question

Find the solution of the system of equations.
10, x, plus, y, equals, minus, 45
10x+y=
−45
2, x, plus, y, equals, minus, 5
2x+y=
−5

Answer 1

To solve the system of equations:

1. \( 10x + y = -45 \) (Equation 1)
2. \( 2x + y = -5 \) (Equation 2)

We can use the substitution or elimination method. Here, we'll use the elimination method by subtracting Equation 2 from Equation 1:

### Step 1: Align the equations

- Equation 1: \( 10x + y = -45 \)
- Equation 2: \( 2x + y = -5 \)

### Step 2: Subtract Equation 2 from Equation 1

\[
(10x + y) - (2x + y) = -45 - (-5)
\]

This simplifies to:

\[
10x - 2x + y - y = -45 + 5
\]

\[
8x = -40
\]

### Step 3: Solve for \( x \)

\[
x = \frac{-40}{8} = -5
\]

### Step 4: Substitute \( x \) back into one of the original equations to find \( y \)

We can substitute \( x = -5 \) into Equation 2:

\[
2(-5) + y = -5
\]

\[
-10 + y = -5
\]

### Step 5: Solve for \( y \)

\[
y = -5 + 10 = 5
\]

### Final solution

The solution to the system of equations is:

\[
x = -5, \quad y = 5
\]

Thus, the ordered pair \((x, y)\) is:

\[
\boxed{(-5, 5)}
\]