# PSAT 1.23 Math Diagnostic

PSAT 1.23 Math Diagnostic. Which of the following would cause the system to have infinite solutions?

 Math Passport to Advanced Math PSAT PSAT Math Diagnostic PSAT Math Math Diagnostic

### Transcript

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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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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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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