Finish solving the system of equations –9.5x – 2.5y = –4.3 and 7x + 2.5y = 0.8 using the linear combination method.

Question

1. Determine which variable will be eliminated:  y will be eliminated because –2.5y and 2.5y are opposite terms.

2. Add the equations together to create a one-variable linear equation:   –2.5x = –3.5

3. Solve to determine the unknown variable in the equation:        x = 1.4

4. Substitute the value of the variable into either original equation to solve for the other variable.

The solution to the system is (
,
).

Answer 1

Let's complete the solution by following the steps you have outlined:

1. You decided to eliminate \(y\), and you are correct since \(-2.5y\) and \(2.5y\) are opposites.

2. Now, add the equations together:

   \[ -9.5x - 2.5y + 7x + 2.5y = -4.3 + 0.8 \]

   The \(y\) terms cancel out:

   \[ (-9.5x + 7x) = -4.3 + 0.8 \]

   \[ -2.5x = -3.5 \]

3. Now, solve for \(x\):

   \[ x = \frac{-3.5}{-2.5} = \frac{3.5}{2.5} = 1.4 \]

4. Substitute \(x = 1.4\) into one of the original equations to solve for \(y\). Let's use the second equation:

   \[ 7x + 2.5y = 0.8 \]

   Substituting \(x = 1.4\):

   \[ 7(1.4) + 2.5y = 0.8 \]

   Calculate \(7(1.4)\):

   \[ 9.8 + 2.5y = 0.8 \]

   Now, isolate \(2.5y\):

   \[ 2.5y = 0.8 - 9.8 \] \[ 2.5y = -9.0 \]

   Now, solve for \(y\):

   \[ y = \frac{-9.0}{2.5} = -3.6 \]

So, the solution to the system of equations is:

\[ \boxed{(1.4, -3.6)} \]