Question

solve the following system of equations using the elimination method 2x + y equals 3.5 and -2 + 2 y equals 2.5

Answer 1

To solve the given system of equations using the elimination method, we first rewrite the equations clearly:

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

We can simplify Equation 2:

\[
-2 + 2y = 2.5
\]

Adding 2 to both sides gives us:

\[
2y = 4.5
\]

Dividing both sides by 2 gives:

\[
y = 2.25 \quad \text{(Equation 3)}
\]

Now we substitute the value of \( y \) from Equation 3 into Equation 1:

\[
2x + 2.25 = 3.5
\]

Next, we isolate \( 2x \) by subtracting 2.25 from both sides:

\[
2x = 3.5 - 2.25
\]
\[
2x = 1.25
\]

Now, dividing both sides by 2 gives:

\[
x = \frac{1.25}{2} = 0.625 \quad \text{(Equation 4)}
\]

So the solution to the system of equations is:

\[
x = 0.625, \quad y = 2.25
\]

In ordered pair form, the solution is:

\[
(0.625, 2.25)
\]