How to find the solution (x,y)

  • Thread starter homevolend
  • Start date
In summary, the solution (x,y) of the system of equations defined by x-y=1 and 2x+y=-4 is the point of intersection between the two lines represented by these equations. To find this solution, one can solve for y in terms of x in one equation, and then substitute that into the other equation to solve for x. The resulting values of x and y will satisfy both equations simultaneously and represent the coordinates of the solution point.
  • #1
homevolend
47
0

Homework Statement



The solution (x,y) of the system equations define by x-y=1 and 2x+y= -4 is what

Homework Equations





The Attempt at a Solution



I found x and y intercepts of these and plotted it but don't know what it means by finding the solution.
 
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  • #2
Finding a solution means finding value(s) of x and y that satisfy both equations simultaneously.

Geometrically, it means finding the intersection of the two lines given by the equations you listed.

Why don't you start by choosing one of the equations, and solving for y in terms of x. Then try substituting that into the other equation.
 
  • #3
y =

2 [x-y=1]
-1 [2x+y=-4]

2x-2y=2
-2x-y=4
--------
-3y=6
y=-2


1[x-y=1]
1[2x+y=-4]

x-y=1
2x+y=-4
--------
-x=-3
x=3 I think I did x wrong somehow but don't know what, but I think I did y right.


like that??
 
  • #4
homevolend said:
y =

2 [x-y=1]
-1 [2x+y=-4]

2x-2y=2
-2x-y=4
--------
-3y=6
y=-2


1[x-y=1]
1[2x+y=-4]

x-y=1
2x+y=-4
--------
-x=-3
x=3 I think I did x wrong somehow but don't know what, but I think I did y right.


like that??

Everything looked OK until this part:

x-y=1
2x+y=-4
--------
-x=-3

This is wrong because x + 2x does not equal -x.
 
  • #5
homevolend said:
x-y=1
2x+y= -4

You can add the equations: y will cancel.

ehild
 

1. How do I solve for x and y in an equation?

Solving for x and y in an equation involves using algebraic manipulation and solving for each variable separately. You can use techniques such as substitution, elimination, or graphing to find the solution.

2. What is the importance of finding the solution (x,y) in a scientific experiment?

Finding the solution (x,y) in a scientific experiment is important because it helps us understand the relationship between variables and how they affect each other. It allows us to make predictions and draw conclusions about the behavior of a system.

3. Can I use a calculator to find the solution (x,y) of an equation?

Yes, you can use a calculator to find the solution (x,y) of an equation. There are many online calculators or graphing calculators that can help you solve equations easily.

4. How do I know if my solution (x,y) is correct?

You can check if your solution (x,y) is correct by substituting the values of x and y into the original equation and seeing if it satisfies the equation. If it does, then your solution is correct.

5. Are there any shortcuts or tricks for finding the solution (x,y) of an equation?

There are some common techniques and strategies for solving equations, such as factoring, completing the square, and using the quadratic formula. These can help simplify the process of finding the solution (x,y) in certain types of equations.

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