Answer :

apologiabiology
an equvilent equation
remember you can do anything to an equation as long asyou do it to both sides


assuming yo have
x+y=1 and
x-3y=9
mulitply both by 2
2x+2y=2
2x-6y=18
those are equvilent



ok, solve initial

x+y=1
x-3y=9
multiply first equation by -1 and add to 2nd equation


-x-y=-1
x-3y=9 +
0x-4y=8

-4y=8
divide both sides by -4
y=-2

sub back
x+y=1
x-2=1
add 2
x=3


x=3
y=-2
(3,-2)

if we test it in other one

2x+2y=2
2(3)+2(-2)=2
6-4=2
2=2
yep

2x-6y=18
2(3)-6(-2)=18
6+12=18
18=18
yep


solution is (3,-2)
equivalent system is the same set of eqns n has the same solution

so for x + y = 1 and x + 3y = 9

an equivalent system can be created by multiplying everything by 3

3x + 3y = 3 and 3x + 9y = 27

solving by substracting one from the other

9y - 3y = 27 - 3

6y = 24

y = 4

x = 1 - y = 1 - 4

= -3

substituting (-3,4) back into

x + y = 1 and x + 3y =9

-3 + 4 = 1 and -3 + 3*4 = 9

so the solutions are good

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