Let's solve the system of equations step by step.
Step 1: Add the equations
Given the equations:
- \( 5x - 4y = -23 \)
- \( -5x - y = -12 \)
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:
\[ \boxed{(1, 7)} \]
1 answer