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(source: China 1997)

Problem 1. (CHINA 1997)

Given that $x=2$ and $y=2$ is the solution of the system $$ ax+by=7\\ bx+cy=5 $$ Then the relation between $a$ and $c$ is

a. $4a+c=9$

b. $2a+c=9$

c. $4a-c=9$

d. $2a-c=9$

My attempt:

I tried subtracting the equations, yielding $2a-2c=2$, or $a-c=1$. Then I got stuck

Andrei
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Carolyn
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    I think you are right and the answers are wrong. – Adam Rubinson Nov 22 '21 at 22:06
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    The question has no valid answer. Choose for example $c=0$, $b=5/2$, $a=1$. – Andrei Nov 22 '21 at 22:06
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    The most obvious way to get $9$ on the right hand side is by multiplying the first equation by $2$ and subtracting the second one. This works well if $x=2$ and $y=1$, to get rid of the term with $b$. This leads to $4a-c=9$. So answer $(c)$ was presumably intended, but there was a typo. – M. Wind Nov 23 '21 at 02:51

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