Let's continue solving the system of equations step-by-step, following the elimination method as indicated:
Given system of equations:
[tex]\[ -9.5x - 2.5y = -4.3 \][/tex]
[tex]\[ 7x + 2.5y = 0.8 \][/tex]
### Step-by-Step Solution:
1. Eliminate [tex]\( y \)[/tex]:
The coefficients of [tex]\( y \)[/tex] are already opposites ([tex]\(-2.5y\)[/tex] and [tex]\(2.5y\)[/tex]), so we can add the equations directly to eliminate [tex]\( y \)[/tex].
2. Add the equations together:
[tex]\[
(-9.5x - 2.5y) + (7x + 2.5y) = -4.3 + 0.8
\][/tex]
Simplify:
[tex]\[
-2.5x = -3.5
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3.5}{-2.5}
\][/tex]
Simplifying:
[tex]\[
x = 1.4
\][/tex]
4. Substitute the value of [tex]\( x \)[/tex] into either original equation:
We can use the second equation for convenience:
[tex]\[
7x + 2.5y = 0.8
\][/tex]
Substitute [tex]\( x = 1.4 \)[/tex] into the equation:
[tex]\[
7(1.4) + 2.5y = 0.8
\][/tex]
Simplify:
[tex]\[
9.8 + 2.5y = 0.8
\][/tex]
Isolate [tex]\( y \)[/tex]:
[tex]\[
2.5y = 0.8 - 9.8
\][/tex]
[tex]\[
2.5y = -9.0
\][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{-9.0}{2.5}
\][/tex]
[tex]\[
y = -3.6
\][/tex]
Therefore, the solution to the system is:
[tex]\[
\boxed{(1.4, -3.6)}
\][/tex]
