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

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

QUESTION POSTED 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

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

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

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