Question

Solve the following system of equations using the elimination method.

2x + y = 3.5 , −x + 2y = 2.5

(_,_)

Answer 1

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 \( (0.9, 1.7) \).