Question

5x-4y=-23
-5x-y=-12
step 1. add the elements
new equation equals?

step 2. solve the new equation finding x and y
step 3. plug y back in to find x write equation showing the substitute steps
step 4. final solution wright as ordered pair

Answer 1

Let's solve the system of equations step by step.

### Step 1: Add the equations
Given the equations:
1. \( 5x - 4y = -23 \)
2. \( -5x - y = -12 \)

We can add these two equations directly:

\[
(5x - 4y) + (-5x - y) = -23 + (-12)
\]

This simplifies to:

\[
0x - 5y = -35
\]

So, the new equation is:

\[
-5y = -35
\]

### Step 2: Solve the new equation for y
To solve for \( y \), divide both sides of the equation by -5:

\[
y = \frac{-35}{-5} = 7
\]

### Step 3: Plug y back into one of the original equations to find x
Now, we will substitute \( y = 7 \) back into one of the original equations. Let's use the second equation:

\[
-5x - y = -12
\]

Substituting \( y = 7 \):

\[
-5x - 7 = -12
\]

To isolate \( x \), first add \( 7 \) to both sides:

\[
-5x = -12 + 7
\]
\[
-5x = -5
\]

Now, divide both sides by -5:

\[
x = 1
\]

### Step 4: Write the final solution as an ordered pair
The solution to the system of equations is:

\[
(x, y) = (1, 7)
\]

So the final solution is:

\[
\boxed{(1, 7)}
\]