How to do these type of math problems (please explain with steps) 10points!!

2x + y = 1
x + y = 2

2x + y = 1 ----> -2x - y = -1 {multiplied top equation by -1}
x + y = 2 -------> x + y = 2 {bottom equation stays the same}

-x = 1 {added the two equations together}
x = -1 {divided both sides by -1}

x + y = 2 {bottom equation}
-1 + y = 2 {substituted -1, in for x, into bottom equation}
y = 3 {added 1 to both sides}

x = -1 and y = 3

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steps in words:
first you need to eliminate one of the values ( doesn't matter x or y)
but in the case getting rid of the "y" is easier
so you subtract y in both equations
then subtract 2x and x which is equal 1x or x
and subtract 1 and 2 you will get -1
x= -1

now once you find the x value put it in one of the equation, for example if i put it into the second one
it will be -1 + y =2 add 1 on both side you will get y =3, then put the into coordinates point
steps in numbers:
2x + y = 1
x + y = 2

2x+y = 1
--
x+ y = 2
x = -1

-1 + y =2
+1 +1
y= 3


(-1,3)

1 - 2x = 2 - x
x = - 1

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

Answer: x = - 1, y = 3

Check—2nd equation:
- 1 + 3 = 2
2 = 2

2x + y = 1
-2(x + y = 2); -2x-2y=-4
-y=-3
y=3
2x+3=1
2x=-2
x=-1
(-1, 3)