To solve the system of equations using the elimination method, we start with the two equations:
- \( 2x + y = 3.5 \) (Equation 1)
- \( -x + 2y = 2.5 \) (Equation 2)
Step 1: Align the equations.
From Equation 1, we have: \[ y = 3.5 - 2x \]
Step 2: Substitute \( y \) in Equation 2.
Substituting for \( y \) in Equation 2 gives: \[ -x + 2(3.5 - 2x) = 2.5 \]
Step 3: Distribute and combine like terms.
Now, distribute: \[ -x + 7 - 4x = 2.5 \] Combine like terms: \[ -5x + 7 = 2.5 \]
Step 4: Solve for \( x \).
Subtract 7 from both sides: \[ -5x = 2.5 - 7 \] \[ -5x = -4.5 \]
Now divide by -5: \[ x = \frac{-4.5}{-5} = 0.9 \]
Step 5: Substitute \( x \) back to find \( y \).
Substituting \( x = 0.9 \) back into Equation 1: \[ 2(0.9) + y = 3.5 \] \[ 1.8 + y = 3.5 \] Subtract 1.8 from both sides: \[ y = 3.5 - 1.8 = 1.7 \]
Final answer:
The solution to the system of equations is: \[ (x, y) = (0.9, 1.7) \]
So, the ordered pair is \( (0.9, 1.7) \).