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)

First, we'll manipulate these equations so we can eliminate one of the variables.

Let's manipulate Equation 1 to make the coefficients of \(y\) the same in both equations. We can multiply Equation 1 by 2:

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

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

Now we have the modified system:

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

Next, we'll eliminate \(y\) by subtracting Equation 2 from Equation 3:

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

Simplifying this, we get:

\[
4x + 2y + x - 2y = 7 - 2.5
\]
\[
5x = 4.5
\]

Now, solving for \(x\):

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

Now that we have \(x\), we can substitute this value back into one of the original equations to find \(y\). Let's use Equation 1:

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

This simplifies to:

\[
1.8 + y = 3.5
\]

Now, solving for \(y\):

\[
y = 3.5 - 1.8 = 1.7
\]

So, the solution to the system of equations is:

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

Thus, the solution in ordered pair form is:

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