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what is y=7-x x-y=-3

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2 Answers

Y = 7 -X           (1)
X - Y = -3         ( 2)
 The problem screaming that substitute me from (1) to (2)
  X - ( 7 - X) = -3
  2X - 7 = -3    2X = 40  X =2
  Now substitute X into (1)
   Y = 7 - 2 = 5      Y =5
You probably want to find values for x and y which would make both of those equations work.  If you can find a way to transform one of the equations into a statement with only one variable, then you are on your way to finding the values of x and y which will work for both equations.
Because they are equations, you can add or subtract the same values to both sides of the equal sign and they will stay balanced.
If you added y to both sides of the second equation, you would change it into:
The left side has opposite y values, which add up to 0.  So it can also be written as:
The first statement said that y =7-x, so I would replace the y in the new equation with 7-x:
x=3+ (7-x)
This was our first goal, to remove the y variable and be left with an equation that has only x variables.
Now I would add 3 and 7:
Then I would add x to both sides:
The left side has the same x values, which add up to 2x.  The right side has opposite x values, which add up to 0.  So it becomes:
Divide both sides by 2 and you have:
This was our second goal, to find out how much our single variable was worth.  Now it can be placed into either of our original equations to find out how much the y variable is worth.  If we found the right value for x, it will work in either equation: