the rules of systems of equations?

Question

I'm trying to figure out what steps (or rules) I follow to solve this problem? solve for x & y if x-y=3 then 2x-y=-1
Thank you

Answer 1

x-y =3
x = 3+y

2x - y = -1
2(3+y) - y = -1

6 + y = -1

y = -7
x = 3 + y = -4

Answer 2

the rules are quite simple:

use the = sign as a devide between the two sides.
if something is subtracted on 1 side, you can add it on the other side to make the equation simpler:
e.g. x-y=3 makes x = 3+y

the same goes for multiplications.
mutliplying on 1 side, can be substituded by divison on the other side.
e.g. x * y = 3 makes x = 3 / y

roots and squares, the same.
x² * 4 = 16 makes x² = 16 / 4 and x= SQRT (16/4)

when doing this, the goal usually is to isolate 1 variable on 1 side, and all the numbers on the other, so you can calculate it.

keep in mind the rules of math
roots and squares before multiplication and division before adding and subtracting

Answer 3

Usually when you have 2 unknowns they will provide 2 eqns, 3variables 3 eqns, so on so forth

in your case you have
Eqn 1: x - y = 3
Eqn 2: 2x - y = -1

Your first task is to take either Eqn and rearrange so that you have x on one side of the equal sign and y on the other side. We'll take Eqn 1 and rearrange as follows

x - y = 3 add y to both sides of the equal sign
x - y + y = 3 + y
x = 3 + y

you now have x on one side and y on the otherside of the equal sign.

Put x = 3 + y into Eqn 2

"A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." G.H. Hardy

Answer 4

x - y = 3
2x - y = - 1

The idea is to move the equations as a pair and then ADD as follows:-

- x + y = - 3 (after multiplying by -1)
2x - y = -1

Now ADD the equations:-
x = - 4

From above x - y = 3
so (-4) - y = 3
- 4 - 3 = y
y = -7

Answer 5

x-y=3........1
2x-y=-1.......2

eq1x2=2x-2y=6......3

eq2x1=2x-y=-1........4

eq3-eq4=(2x-2y=6) - (2x-y=-1)

or-y=7
putting y in (1)
x-7=3
orx=10
ans.y=-7
x=10