Posted by Catherine on Friday, January 25, 2008 at 9:27pm.
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Homework Help Forum: Math
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Posted by Catherine on Friday, January 25, 2008 at 9:27pm.
12x+4y= 22 and 3x-8y= -10
What are the coordinates of x and y? Use the Substitution Method.
For the first one.
12x+4y=22
3x-8y=-10
=============
I would solve equation 2 for x as
x=(-10+8y)/3
Then substitute this for x in equation 1 as
12[(-10+8y)/3] + 4y = 22
4(-10+8y) + 4y = 22
-40 + 32y + 4y = 22
36y = 40 + 22
36y = 62 + 40 = 62
y = 62/36 = 31/18
a strange number but it's right I think.
You substitute this value for y into equation 2 and solve for x. I found x to be 34/27, another strange number, but I think it's right. That's how you do these things. I'll leave the other one for you. Post specific questions if you get stuck. By the way, I substituted 31/18 for x and 34/27 for y and it checks. Check my work,especially for typos.
y = 30/36 =
---and---
-5x+7y= -41 and 7x+y=25
What are the coordinates of x and y? Use the Substitution Method
I don't know why my post copied all that extra trash but the part you want to read is in bold (except for the last y = 30/36 which has nothing to do with your problem). I'm pleased that Damon obtained the same strange numbers I did.
12x+4y= 22 and 3x-8y= -10
These are both equations of lines and if they are not the same or parallel they will cross each other at one point, giving you a spot with x, y coordinates.
To solve it by substitution, solve either equation for either x or y and use that in the other equation. Then go back and find the value of the substituted variable with either original.
For example:
1.
solve the first equation for y
4 y = -12 x + 22
so
y = (-3 x + 11/2)
2.
Use that y in your second equation to get x
3 x - 8(-3x + 11/2) = -10
3 x + 24 x - 44 = -10
27 x = 34
x = 34/27
3.
use x = 34/27 in either original, like the first, to get y
12 (34/27) + 4 y = 22
136/9 + 4 y = 22
4 y = 62/9
y = 31/18
So, our intersection point is (34/27,32/18)
I checked the strange numbers back. They worked.
I did too because I didn't believe them (until I checked).
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