Question

Two lines have the given equations. Use the Linear Combination Method to solve.

Answer 1

Answer:

$\large{\textbf{(x,y) = (-7, -15)}\\}$

Step-by-step explanation:

$\large{\textup{The given equations represent two straight lines.}}\\\\ \large{\textup{To solve them is to find the \textbf{point of intersection} of the two lines.}}$

$\begin{align*}\\2x - y &= 1 \hspace{25mm} (1) \\3x - y &= -6 \hspace{24mm} (2) \\\end{align*}$

$\large{ \textup{We start by eliminating one variable.}}$

$\textup{In this case, y can be eliminated by subtracting (1) \& (2).}}}$

$\large{\textup{We get}\\}$

$\begin{align*}2x - y &= 1 \\-3x + y &= 6 \\\implies -x &= 7\\\implies x &= -7\end{align*}$

$\large{\textup{Substituting x = -7 in (1) , we get:} 2(-7) - 1 = y \\ \implies y = -15 \\\textup{Therefore, x= -7, y = -15 }\\\textup{Simply put, (x,y) = (-7,-15) is the point of intersection of (1) \& (2) }.}$