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PSAT 1.23 Math Diagnostic 195 Views


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Description:

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


Transcript

00:00

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

00:05

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

00:09

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

00:12

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

00:15

b which of the following if added to the equation

00:17

above to form a system of equations would cause the

00:20

system to have infinite solutions and hear the potential answered

00:23

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

00:27

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

00:30

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

00:33

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

00:36

each one couple it with the given equation to make

00:38

a system of equations and then go from there when

00:40

we find the answer choice that results in an infinite

00:42

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

00:46

second thought All these answer choice and looked pretty gender

00:49

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

00:51

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

00:54

equation Negative to a plus five equals b Well we

00:56

already have something we can substitute as b This thing

00:59

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

01:02

and we get ten plus two times quantity negative to

01:04

eight plus five equals for a almost like through It

01:07

simplifies to ten months for a plus ten equals for

01:10

a we can add our tends together to get twenty

01:13

and then add foray to both sides to get twenty

01:16

equals a divide Both sides by eight and eight equals

01:19

twenty over eight or five half way get a solution

01:22

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

01:25

was right Option b a dear john letter and move

01:27

on with our lives How about c a day plus

01:30

four b equals fifty six Well again we can take

01:33

negative to a plus five and substitute that for b

01:35

way Get a day plus four times the quantity negative

01:38

to a plus five equals fifty six Multiply through a

01:41

day minus a day plus twenty equals fifty six are

01:44

eight days cancel and it looks like twenty equals fifty

01:48

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

01:51

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

01:56

so we can cross it off our list What about

01:58

option d A plus B equals negative one Well you

02:00

know the real when we substitute this becomes a plus

02:03

The quantity negative to a plus five equals negative one

02:06

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

02:09

and subtract five from both sides and negative equals negative

02:13

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

02:16

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

02:18

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

02:21

a can turn things around while sixty equals fifteen minus

02:24

three b will substitute yet again Get six a equals

02:28

fifteen minus three times the quantity Negative to a plus

02:33

five Multiply through to get six a equals fifteen plus

02:36

six A minus fifteen are fifteen Cancel And now we

02:40

have six A equals six eh Well yeah Duh No

02:43

matter what value we plug in for a this equation

02:46

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

02:49

two or dog This equation will check out Which means

02:52

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

02:55

try a few hundred thousand of them To be sure

02:57

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

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