I'm learning about Equivalent systems of equations, please help!

QUESTION POSTED AT 02/12/2019 - 07:55 AM

Answered by answersmine AT 02/12/2019 - 07:55 AM

OK to solve this, we have to solve each system presented through elimination or substitution and find which one is equivalent to that of the teacher's!

First let's solve for the teacher's:
-2x+5y=10
-3x+9y=6
Solve by substitution (I think elimination might be easier to do for this one, but I don't really remember 100% sorry!)
Isolate the x (or y) variable in the first equation
-2x+5y=10
-2x=10-5y
x= \frac{10-5y}{-2}
Substitute x into the next equation and solve for y
-3(10-5y/2)+9y=6
3*10-5y/2+9y=6
(multiply both sides by 2)
3(10-5y)+18y=12
30-15y+18y=12
30+3y=12
3y=-18
y=-6

Substitute in x
x= -10-5(-6)/2
x=-20

TEACHER'S ANSWER (-20,-6)


GOKU
x-3y=-2
-2x+5y=-7
Do the same as above
Solve for x
x-3y=-2
x=3y-2
Plug in
-2(3y-2)+5y=-7
4-6y+5y=-7
4-y=-7
-y=-11
y=11

x=(3(11)-2)
x=31
GOKU'S ANSWER (31, 11)

SELINA:
-5x+14y=16
-3x+9y=12
One last time!! :)

-5x+14y=16
-5x=16-14y
x=(16-14y)/-5

-3(-(16-14y/5)+9y=12
3*16-14y/5+9y=12
3*16-14y+45y=60 
48-42y+45y=60
48+3y=60
3y=12
y=4

x=-(16-14(4))/5
x=8
SELINA'S ANSWER
(8,4)

So neither Goku or Selina got the same answer as the teacher
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