# Solve for: {\text{begin}array l 8x-5y=7 } 16x-10y=14\text{end}array .

## Expression: $\left\{\begin{array} { l } 8x-5y=7 \\ 16x-10y=14\end{array} \right.$

Move the variable to the right-hand side and change its sign

$\left\{\begin{array} { l } 8x=7+5y \\ 16x-10y=14\end{array} \right.$

Move the variable to the right-hand side and change its sign

$\left\{\begin{array} { l } 8x=7+5y \\ 16x=14+10y\end{array} \right.$

Divide both sides of the equation by $2$

$\left\{\begin{array} { l } 8x=7+5y \\ 8x=7+5y\end{array} \right.$

Since both expressions $7+5y$ and $7+5y$ are equal to $8x$, set them equal to each other forming an equation in $y$

$7+5y=7+5y$

Solve the equation for $y$

$y \in ℝ$

The statement is true for any value of $y$ and $x$ that satisfy both equations from the system. Therefore, the solution in parametric form is

$\begin{array} { l }\left( x, y\right)=\left( \frac{ 7 }{ 8 }+\frac{ 5 }{ 8 }y, y\right),& y \in ℝ\end{array}$

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