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# Proportions Problem

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In a rectangular coordinate system, the line $3y = x$ intersects the line $2x + 5y = 11$ at point $A$. What is the sum of the coordinates of point $A$? Please do a full walkthrough.

Jul 17, 2022

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We have the system:

$$2x + 5y = 11 \ \ \ \ \ \ \ (i)$$

$$3y = x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (ii)$$

Start by substituting $$(ii)$$ into $$(i)$$, which gives us $$2(3y) + 5y = 11$$, meaning $$y = 1$$

Now, plug in $$y = 1$$ into $$(ii)$$, to get $$3 \times 1 = x$$, meaning $$x = 3$$.

This means that the solution is $$(3,1)$$, meaning the sum is $$3 + 1 = \color{brown}\boxed{4}$$

Jul 17, 2022