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

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PSAT Math | Math Diagnostic |

above to form a system of equations would cause the

system to have infinite solutions and hear the potential answered

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

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

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

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

each one couple it with the given equation to make

a system of equations and then go from there when

we find the answer choice that results in an infinite

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

second thought All these answer choice and looked pretty gender

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

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

equation Negative to a plus five equals b Well we

already have something we can substitute as b This thing

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

and we get ten plus two times quantity negative to

eight plus five equals for a almost like through It

simplifies to ten months for a plus ten equals for

a we can add our tends together to get twenty

and then add foray to both sides to get twenty

equals a divide Both sides by eight and eight equals

twenty over eight or five half way get a solution

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

was right Option b a dear john letter and move

on with our lives How about c a day plus

four b equals fifty six Well again we can take

negative to a plus five and substitute that for b

way Get a day plus four times the quantity negative

to a plus five equals fifty six Multiply through a

day minus a day plus twenty equals fifty six are

eight days cancel and it looks like twenty equals fifty

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

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

so we can cross it off our list What about

option d A plus B equals negative one Well you

know the real when we substitute this becomes a plus

The quantity negative to a plus five equals negative one

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

and subtract five from both sides and negative equals negative

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

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

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

a can turn things around while sixty equals fifteen minus

three b will substitute yet again Get six a equals

fifteen minus three times the quantity Negative to a plus

five Multiply through to get six a equals fifteen plus

six A minus fifteen are fifteen Cancel And now we

have six A equals six eh Well yeah Duh No

matter what value we plug in for a this equation

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

two or dog This equation will check out Which means

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

try a few hundred thousand of them To be sure

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