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

1 answer

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:

\[ (0.625, 2.25) \]