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Geometry Difficulty 3.9 AMC 10/12 Find the answer United States

Problem:
The graphs of the equations
$\begin{aligned} y & = -x + 8 \\ 173y & = -289x + 2021 \end{aligned}$
on the Cartesian plane intersect at $(a, b)$ . Find $a + b$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:
From the first equation, it is known that $(a, b)$ lies on the line $x + y = 8$ , therefore $a + b = 8$ .

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