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Use your solution from Question 1 to find integers 𝑥 and 𝑦 such that 875𝑥 + 4075𝑦 = 50.

by admin|Published April 27, 2026

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Question 2

Use your solution from Question 1 to find integers $x$ and $y$ such that $875x + 4075y = 50$ .

Theorem. If $(a,b)=d$ , then there exist integers $x,y$ such that $ax + by = d$ .

From Q1 (Euclidean Algorithm):

$4075 = 4(875) + 575$
$875 = 1(575) + 300$
$575 = 1(300) + 275$
$300 = 1(275) + 25$
$300 = 25(12) + 0$

Work the Euclidean Algorithm backwards:

$25 = 300 - 275$
$25 = 300 - (575 - 300)$
$25 = 2(300) - 575$
$25 = 2(875 - 575) - 575$
$25 = 2(875) - 3(575)$
$25 = 2(875) - 3(4075 - 4(875))$
$25 = 14(875) - 3(4075)$

Multiply both sides by 2:

$50 = 28(875) - 6(4075)$

Therefore, $x = 28$ , $y = -6$ .

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