Solving for X and Y, I cant figure out how to do it
- Thread starter amaris
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mmm4444bot
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These exercises require solving each of the three "system of equations". (There are different ways to solve such systems; I'm not sure which methods you're studying.)
I'll do the first one, using a basic method; the strategy is to first solve each equation for y. Then set the results equal to one another, and solve for x. Once we know x, it's easy to find y.
The first equation is 2x - y = 5. If we solve this equation for y, we get y = 2x - 5.
The second equation is x + 2y = 10. If we solve this equation for y, we get y = -(1/2)x + 5.
Since the right-hand side of these results are both equal to y, they are equal to each other (y = y, correct?).
2x - 5 = -(1/2)x + 5
This equation contains only one variable (x), so we can solve for it.
x = 4
Now that we know x, we find y by substitution.
y = 2(4) - 5
y = 3
Check the solution x = 4 and y = 3, using the given equations.
2(4) - 3 = 5
8 3 = 5
5 = 5
4 + 2(3) = 10
4 + 6 = 10
10 = 10
The solution checks.
If you need more help, please ask specific questions and show your work.
I'll do the first one, using a basic method; the strategy is to first solve each equation for y. Then set the results equal to one another, and solve for x. Once we know x, it's easy to find y.
The first equation is 2x - y = 5. If we solve this equation for y, we get y = 2x - 5.
The second equation is x + 2y = 10. If we solve this equation for y, we get y = -(1/2)x + 5.
Since the right-hand side of these results are both equal to y, they are equal to each other (y = y, correct?).
2x - 5 = -(1/2)x + 5
This equation contains only one variable (x), so we can solve for it.
x = 4
Now that we know x, we find y by substitution.
y = 2(4) - 5
y = 3
Check the solution x = 4 and y = 3, using the given equations.
2(4) - 3 = 5
8 3 = 5
5 = 5
4 + 2(3) = 10
4 + 6 = 10
10 = 10
The solution checks.
If you need more help, please ask specific questions and show your work.
D
Deleted member 4993
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amaris said:
I'll do one for you:
2x - y = 5 ...........................................(1)
x + 2y = 10..........................................(2)
Multiply (1) by "2" and add to (2): <<<< Edited
2{2x - y} +{x +2y} = 2*5 + 10
5x = 20
x = 4
Use this value of 'x' in (1) and solve for 'y'
Then check your work by sustituting both 'x' & 'y' into (1) & (2).
dbngshuroy
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amaris said:
Is these are 3 different equations? or a system of equations?
D
Deleted member 4993
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fausts said:
What method have you been taught to solve such equation?
I have solved - more than halfway, with strong hints regarding how to solve rest of it - one of the problems in a previous post (in this thread).
Why are not you able start the others? What have you tried?
For a quick review, go to:
http://www.purplemath.com/modules/systlin4.htm
Following the worked out problems in that web-site, you should be able get started and finished.
Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
mmm4444bot
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fausts said:
I see that you quoted amaris' exercises. If those are the exercises that you're asking about, then you could start by studying the second and third posts in this thread.