To solve the system of equations:
[tex]\[
\begin{align*}
1) \quad y &= 2x - 3.5 \\
2) \quad x - 2y &= -14
\end{align*}
\][/tex]
we need to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations simultaneously.
### Step 1: Substitute [tex]\( y \)[/tex] from Equation 1 into Equation 2
Given:
[tex]\[ y = 2x - 3.5 \][/tex]
Substitute [tex]\( y \)[/tex] in Equation 2:
[tex]\[ x - 2(2x - 3.5) = -14 \][/tex]
### Step 2: Simplify the resulting equation
[tex]\[
x - 2(2x - 3.5) = -14
\][/tex]
[tex]\[
x - 2 \cdot 2x + 2 \cdot 3.5 = -14
\][/tex]
[tex]\[
x - 4x + 7 = -14
\][/tex]
Combine like terms:
[tex]\[
-3x + 7 = -14
\][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
[tex]\[
-3x + 7 = -14
\][/tex]
Subtract 7 from both sides:
[tex]\[
-3x = -14 - 7
\][/tex]
[tex]\[
-3x = -21
\][/tex]
Divide both sides by -3:
[tex]\[
x = 7
\][/tex]
### Step 4: Substitute [tex]\( x \)[/tex] back into Equation 1 to find [tex]\( y \)[/tex]
Using [tex]\( x = 7 \)[/tex] in the equation [tex]\( y = 2x - 3.5 \)[/tex]:
[tex]\[
y = 2(7) - 3.5
\][/tex]
[tex]\[
y = 14 - 3.5
\][/tex]
[tex]\[
y = 10.5
\][/tex]
### Conclusion
The solution to the system of equations is:
[tex]\[
(x, y) = (7, 10.5)
\][/tex]
Therefore, the correct choice is:
[tex]\[
(7, 10.5)
\][/tex]
