Solve the following system of equations using the elimination method.

Question

2x+y=3.5
2
𝑥
+
𝑦
=
3.5

−x+2y=2.5
−
𝑥
+
2
𝑦
=
2.5

(1 point)
( , )

Answer 1

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

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

Step 1: Eliminate \( y \)

First, we can manipulate Equation 1 to express \( y \) in terms of \( x \):

From Equation 1: \[ y = 3.5 - 2x \]

Now, substitute this expression for \( y \) into Equation 2:

\[ -x + 2(3.5 - 2x) = 2.5 \]

Step 2: Simplify and solve for \( x \)

Distributing the 2: \[ -x + 7 - 4x = 2.5 \]

Combining like terms: \[ -5x + 7 = 2.5 \]

Subtracting 7 from both sides: \[ -5x = 2.5 - 7 \] \[ -5x = -4.5 \]

Dividing by -5: \[ x = \frac{-4.5}{-5} = 0.9 \]

Step 3: Substitute \( x \) back to find \( y \)

Now that we have \( x \), substitute \( x = 0.9 \) back into the expression for \( y \): \[ y = 3.5 - 2(0.9) \] \[ y = 3.5 - 1.8 \] \[ y = 1.7 \]

Solution

The solution to the system of equations is: \[ (x, y) = (0.9, 1.7) \]

Thus, the final answer is: \[ (0.9, 1.7) \]