Question

Solve the following system equations using the elimination method 2x + y = 3.5, negative X + 2y = 2.5

Answer 1

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

1) \( 2x + y = 3.5 \)
2) \( -x + 2y = 2.5 \)

### Step 1: Align the equations
We can multiply the first equation by 2 to facilitate elimination of \( y \):

\[
4x + 2y = 7 \quad \text{(equation 1 multiplied by 2)}
\]

So, we now rewrite our system:

1) \( 4x + 2y = 7 \)
2) \( -x + 2y = 2.5 \)

### Step 2: Subtract the second equation from the first
Now we can eliminate \( y \) by subtracting the second equation from the first:

\[
(4x + 2y) - (-x + 2y) = 7 - 2.5
\]

This simplifies to:

\[
4x + 2y + x - 2y = 7 - 2.5
\]

Combining like terms gives:

\[
5x = 4.5
\]

### Step 3: Solve for \( x \)
Dividing both sides by 5:

\[
x = \frac{4.5}{5} = 0.9
\]

### Step 4: Substitute \( x \) back into one of the original equations
Now, we substitute \( x = 0.9 \) back into the first equation to find \( y \):

\[
2(0.9) + y = 3.5
\]

This simplifies to:

\[
1.8 + y = 3.5
\]

Subtracting 1.8 from both sides gives:

\[
y = 3.5 - 1.8 = 1.7
\]

### Conclusion
The solution to the system of equations is:

\[
x = 0.9, \quad y = 1.7
\]

So the final answer is:

\[
(x, y) = (0.9, 1.7)
\]