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)
First, we'll manipulate these equations so we can eliminate one of the variables.
Let's manipulate Equation 1 to make the coefficients of \(y\) the same in both equations. We can multiply Equation 1 by 2:
\[ 2(2x + y) = 2(3.5) \] This gives us:
\[ 4x + 2y = 7 \quad \text{(Equation 3)} \]
Now we have the modified system:
- \( 4x + 2y = 7 \) (Equation 3)
- \(-x + 2y = 2.5 \) (Equation 2)
Next, we'll eliminate \(y\) by subtracting Equation 2 from Equation 3:
\[ (4x + 2y) - (-x + 2y) = 7 - 2.5 \]
Simplifying this, we get:
\[ 4x + 2y + x - 2y = 7 - 2.5 \] \[ 5x = 4.5 \]
Now, solving for \(x\):
\[ x = \frac{4.5}{5} = 0.9 \]
Now that we have \(x\), we can substitute this value back into one of the original equations to find \(y\). Let's use Equation 1:
\[ 2(0.9) + y = 3.5 \]
This simplifies to:
\[ 1.8 + y = 3.5 \]
Now, solving for \(y\):
\[ y = 3.5 - 1.8 = 1.7 \]
So, the solution to the system of equations is:
\[ x = 0.9, \quad y = 1.7 \]
Thus, the solution in ordered pair form is:
\[ \boxed{(0.9, 1.7)} \]
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