Create an equivalent system of these equations and test your solution

x + y = 1

x 3y = 9

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