12x+4y= 22 and 3x-8y= -10
What are the coordinates of x and y? Use the Substitution Method.
---and---
-5x+7y= -41 and 7x+y=25
What are the coordinates of x and y? Use the Substitution Method.
Please help!!! =DDD
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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
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 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.
I checked the strange numbers back. They worked.
I did too because I didn't believe them (until I checked).
To solve the systems of equations using the Substitution Method, follow these steps:
1. Solve one equation for one variable in terms of the other variable.
2. Substitute the expression from step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 back into either of the original equations to find the value of the other variable.
5. Write the coordinates as (x, y).
Now, let's solve the given systems of equations using the Substitution Method.
1. First system of equations:
12x + 4y = 22 ---(equation 1)
3x - 8y = -10 ---(equation 2)
2. In equation 2, solve for x in terms of y:
3x = 8y - 10
x = (8y - 10) / 3
3. Substitute the expression for x into equation 1:
12((8y - 10) / 3) + 4y = 22
4. Simplify the equation:
(32y - 40) + 4y = 22
36y - 40 = 22
36y = 62
y = 62 / 36
y ≈ 1.72
5. Substitute the value of y back into equation 2 to find x:
3x - 8(1.72) = -10
3x - 13.76 = -10
3x = 3.76
x = 3.76 / 3
x ≈ 1.25
Therefore, the coordinates of x and y for the first system of equations are approximately (1.25, 1.72).
Now, let's solve the second system of equations.
1. -5x + 7y = -41 ---(equation 1)
7x + y = 25 ---(equation 2)
2. In equation 2, solve for y in terms of x:
y = 25 - 7x
3. Substitute the expression for y into equation 1:
-5x + 7(25 - 7x) = -41
4. Simplify the equation:
-5x + 175 - 49x = -41
-54x + 175 = -41
-54x = -216
x = -216 / -54
x = 4
5. Substitute the value of x back into equation 2 to find y:
7(4) + y = 25
28 + y = 25
y = 25 - 28
y = -3
Therefore, the coordinates of x and y for the second system of equations are (4, -3).
I hope this helps! Let me know if you have any further questions.