# LINR 3 | Lesson 1 | Try This! Solving a System Solution

1.
• Using elimination: $$2x + 3y = 11$$ and $$x + 2y = 6$$ , note that we could eliminate either $$x$$ or $$y$$.   If we want to eliminate $$x$$ we can multiply the second equation through by $$-2$$ and adding them together.

\begin{align} 2x + 3y &= 11 \\\\ -2x-4y &= -12 \\\\ \therefore -y = -1~ &\text{or } y = 1\end{align}

by substituting $$1$$ for $$y$$ in the top equation

$$2x + 3 = 11$$ → $$x = 4$$

$$(4, 1)$$ is the point of intersection.

• Using substitution:  We can solve the second equation for $$x$$; $$x = -2y + 6$$

$$2(-2y + 6) + 3y = 11$$ →$$-4y +12 + 3y = 11$$ ;   $$y = 1$$

and $$2x + 3 = 11$$; $$x = 4$$.   Intersection is at $$(4, 1)$$

• Did you get $$(4,1)$$ when graphing the equations?
1. $$x$$ represents the cost of a ticket and $$y$$ the cost of a container of popcorn.

$$4x +3y = 72$$

$$5x + 3y = 87$$

A ticket costs $$$15$$ and a container of popcorn costs$$$4$$.