Solve the following system of equations using the elimination method.

2x + y = 3.5 , −x + 2y = 2.5

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1 answer

To solve the system of equations using the elimination method, we start with the two equations:

  1. \( 2x + y = 3.5 \) (Equation 1)
  2. \( -x + 2y = 2.5 \) (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 \( (0.9, 1.7) \).