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Problem 717

AMC 10/12, early questions

Geometry Difficulty 3.9 Find the answer HMMT November · United States · 2021

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.

Official 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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