ShmoopTube

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Thank you We sneak And here's your shmoop du jour

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brought to you by infinite solutions We're talking a heck

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of a lot of scratch paper All right let's say

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we're given the equation negative to a plus five equals

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b which of the following if added to the equation

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above to form a system of equations would cause the

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system to have infinite solutions and hear the potential answered

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All right there Wow that's A lot of solutions not

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the contact lens stuff Either We'd stay here to countem

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all but well we've got a thing Well here's where

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It's Awfully nice to have multiple choices waken just take

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each one couple it with the given equation to make

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a system of equations and then go from there when

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we find the answer choice that results in an infinite

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number of solutions We've got our man or woman on

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second thought All these answer choice and looked pretty gender

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neutral there All right Well let's start with b ten

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plus two b equals for a and here's our original

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equation Negative to a plus five equals b Well we

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already have something we can substitute as b This thing

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right here So let's Plug that in Option these equations

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and we get ten plus two times quantity negative to

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eight plus five equals for a almost like through It

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simplifies to ten months for a plus ten equals for

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a we can add our tends together to get twenty

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and then add foray to both sides to get twenty

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equals a divide Both sides by eight and eight equals

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twenty over eight or five half way get a solution

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but only one of them that's it hardly infinite It

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was right Option b a dear john letter and move

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on with our lives How about c a day plus

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four b equals fifty six Well again we can take

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negative to a plus five and substitute that for b

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way Get a day plus four times the quantity negative

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to a plus five equals fifty six Multiply through a

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day minus a day plus twenty equals fifty six are

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eight days cancel and it looks like twenty equals fifty

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six On what planet If we're converting from celsius not

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fahrenheit maybe don't know this one yields zero real solutions

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so we can cross it off our list What about

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option d A plus B equals negative one Well you

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know the real when we substitute this becomes a plus

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The quantity negative to a plus five equals negative one

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We're left with negative A plus five equals negative one

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and subtract five from both sides and negative equals negative

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six Meaning that a equal six We'll get a slight

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upgrade from option c which had no solutions But we're

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still a long way off from infinite here's hoping option

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a can turn things around while sixty equals fifteen minus

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three b will substitute yet again Get six a equals

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fifteen minus three times the quantity Negative to a plus

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five Multiply through to get six a equals fifteen plus

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six A minus fifteen are fifteen Cancel And now we

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have six A equals six eh Well yeah Duh No

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matter what value we plug in for a this equation

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whether it's fourteen twenty seven thirty eight point nine six

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two or dog This equation will check out Which means

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it has infinite solutions Then we don't even have to

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try a few hundred thousand of them To be sure

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So is our answer And that makes us infinitely happy 00:03:00.103 --> [endTime] Seriously check out that Yeah

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