Question

Solve the following system of equations using the elimination method.2x+y=3.5, −x+2y=2.5(1 point)

Answer 1

To solve the system of equations using the elimination method, we have the following equations:

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

First, we can eliminate one of the variables. We'll start by eliminating \( y \).

### Step 1: Make the coefficients of \( y \) the same

To do this, we can multiply Equation 1 by 2, so the coefficient of \( y \) in both equations will be 2.

\[
2(2x + y) = 2(3.5)
\]
This gives us:

\[
4x + 2y = 7 \quad \text{(Equation 3)}
\]

Now our system of equations is:

1. \( 4x + 2y = 7 \) (Equation 3)
2. \( -x + 2y = 2.5 \) (Equation 2)

### Step 2: Eliminate \( y \)

Now, we will subtract Equation 2 from Equation 3 to eliminate \( y \):

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

Simplifying this:

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

\[
5x = 4.5
\]

### Step 3: Solve for \( x \)

Now, we can solve for \( x \):

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

### Step 4: Substitute \( x \) back to find \( y \)

Substituting \( x = 0.9 \) back into Equation 1:

\[
2(0.9) + y = 3.5
\]
This simplifies to:

\[
1.8 + y = 3.5
\]
Subtracting 1.8 from both sides:

\[
y = 3.5 - 1.8 = 1.7
\]

### Solution

The solution to the system of equations is:

\[
\boxed{(0.9, 1.7)}
\]