Help Please

- BioHazard9064

Help Please

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- BioHazard9064

A system of equations is shown below:
-3x + 7y = -16
-9x + 5y = 16
Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this.
Part B: Show that the equivalent system has the same solution as the original system of equations.

- BioHazard9064

@triciaal hey can you help me please

- triciaal

so you need to solve by elimination.

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- BioHazard9064

OK so how do we do that.

- triciaal

the objective is to pick a variable and make the coefficient equal and opposite so that when you add the equations the sum of that variable is zero as in eliminated.
you now have one equation with one variable. solve.
use this value in either of the originals to get the value of the other.

- BioHazard9064

so wait if this is elimination we would add them

- triciaal

i will walk you through this time

- BioHazard9064

to get the x then use the x to get the y

- triciaal

pick a variable

- BioHazard9064

x

- triciaal

so to make the coefficients equal and opposite multiply the first eqn by - 3

- BioHazard9064

ok so that would look something like this 9x+7y=48

- BioHazard9064

am i right?

- triciaal

|dw:1440782571063:dw|

- BioHazard9064

do we subtract -10 with 64?

- triciaal

no you forgot to multiply the 7y

- BioHazard9064

-16*

- triciaal

slow down and follow

- BioHazard9064

ok

- triciaal

now that you have y substitute in either of the originals and calculate x

- BioHazard9064

wait what was our y

- triciaal

it is always a good practice to check the solution in the other original because it is very very easy to make arithmetic errors.

- BioHazard9064

indeed I make them all the time xD

- triciaal

so what was your solution?

- BioHazard9064

for what... what I said earlier?

- BioHazard9064

oh wait so we were supposed to multiply the -3 *7

- triciaal

yes

- BioHazard9064

9x-21=48*

- triciaal

|dw:1440783443270:dw|

- triciaal

you forgot your y

- BioHazard9064

oh yea 9x-21y=48

- triciaal

|dw:1440783530804:dw|

- BioHazard9064

no wait im supposed to divide sorry

- BioHazard9064

y=-4
@triciaal

- triciaal

now find x

- BioHazard9064

-3x + 7(-4) = -16

- BioHazard9064

So we would do +3x

- BioHazard9064

is-int it multiplication

- BioHazard9064

x=-4

- triciaal

go ahead and +3x if that is easier for you
the idea is to isolate the variable terms to one side and the constants to the other then divide by the coefficient of the variable

- BioHazard9064

both of them are -4 right?

- triciaal

correct

- triciaal

solution (-4, -4)

- BioHazard9064

So how would i do this ...
Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this

- triciaal

review everything from the beginning

- BioHazard9064

ok ... I dont see it

- BioHazard9064

like I see what your talking about but I dont see how that is an equivalent system

- BioHazard9064

@triciaal sorry to bother you more but I dont understand

- triciaal

where did you stop?

- BioHazard9064

stop?

- triciaal

did you review?
we have a multiple of equation 1 because we multiplied by -3
we added this to the 2nd eqn
equivalent system created
sum means to add

- triciaal

show it has the same result the solution works in each of the originals

- BioHazard9064

oh yes I did and thanks so much for helping me

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