Posted by Catherine on Friday, January 25, 2008 at 9:27pm.
Subjects
Art
Business
Computers
English
Foreign Languages
Health
Home Economics
Mathematics
Music
Physical Education
Science
Social Studies
Features
Contribute
Download
Experts
Forum
Job Openings
Homework Tips
Libraries.Jiskha
Link to Us
Reference
School Supplies
Search
Homework Help Forum: Math
Current Questions | Post a New Question | Answer this Question | Further Reading
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).