Solve the system!?

Question

x+5/5 + 2y-x/10 =3


x+3/4 + 3y+2/5 = -3

Answer 1

First step 5/5 = 1 right
that gives you x + 1 + 2y -x/10 =3
collect terms and use additive inverse to move 1 to other side of the = sign.

x+1 -1 + 2y -x/10 = 3-1
x+2y -x/10 =2
rearrange:
2y +x- x/10 =2
collect terms remember -x/10 means x divided by 10 or 1x divided by 10.

now collect terms again.

2y +(x -x/10) = 2
factor out x.

2y x(1 - 1/10) =2
simplify: don't forget 1 = 10/10 in fraction form.

2y + x(10/10 -1/10) =2
2y + x(9/10) = 2
next transpose 2y across = sign by using additive inverse:

x(9/10) = 2 - 2y
next factor out 2
x(9/10) = 2(1 - y)
next step transpose the 9/10 by dividing both sides by 9/10.
in fractions recall that means to invert and multiply.

x(9/10) * (10/9) = (2(1 - y) ) * (10/9)

x = 20(1 -y) / 9 or:

20(1 -y)
------------ = x
.......9

another way to state it:

x = 20 / 9 - 20y / 9

Work the second on the same way:

x + 3/4 +3y + 2/5 = -3
x + 3/4 -3/4 + 3y + 2/5 = - 3 - 3/4
x + 3y + 2/5 = -3 - 3/4 have to add so have to convert -3 to a fraction with same denominator as 3/4 which is 4.
that comes out to - 12/4
x+ 3y + 2/5 = - 12/4 - 3/4 since as sign add:

x + 3y + 2/5 = - 15/4
next used additive inverse move 2/5 to other side of = sign.

x + 3y +2/5 - 2/5 = - 15/4 -2/5

x + 3y = - 15/4 -2/5 now have to find the lowest common denominator of 15/4 and 2/5 which is 20:

or convert 15 fours back to a mixed number to make it easier to work problem.

that gives you -3 3/4 - 2/5 making it easier to work:

which gives you:

x + 3y = -3 15/20 - 8/20
now add

x + 3y = - 3 23/20

x + 3y = -4 3/20 or minus 4 and 3/20
depends on how far you are supposed to carry it.