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:

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