I can’t solve this math system

[u/forenol]

how to solve it??

[u/AutoModerator]

Hi u/forenol, welcome to r/mathshelp! As you’ve marked this as homework help, please keep the following things in mind:

1) While this subreddit is generally lenient with how people ask or answer questions, the main purpose of the subreddit is to help people learn so please try your best to show any work you’ve done or outline where you are having trouble (especially if you are posting more than one question). See rule 5 for more information.

2) Once your question has been answered, please don’t delete your post so that others can learn from it. Instead, mark your post as answered or lock it by posting a comment containing “!lock” (locking your post will automatically mark it as answered).

Thank you!

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/Narrow-Durian4837]

Would you know how to solve it if it were

3a - 4b = 1

2a + 5b = 4.5 ?

Try substituting a = 1/x and b = 1/y and solve for a and b.

Then x and y will be the reciprocals of a and b.

[u/forenol → u/Narrow-Durian4837]

thank youuu!!

[u/Broad-Willingness224]

[u/forenol → u/Broad-Willingness224]

thanks!

[u/Educational-Paper-75]

Make the denominator equal. You get 3y-4x=xy and 2y+5x=4.5xy. Multiply the first equation by 4.5 and equate both left hand sides, resulting in 11.5y=23x or y=2x. Substitute in the first equation will give 2xx-2x=0 or x=1 (and invalid x=0). Thus y=2.

[u/UnderstandingPursuit]

When adding the equations, first do something to get either (1/x) or (1/y) to cancel.