Question 114898This question is from textbook Beginning Algebra
: This is a problem from Section 8.1 on page 687. I cannot think backwards, which is what I believe I need to do. The problem is as follows:
Find values for m and b in the following system so that the solution to the system is (-3,4).
5x + 7y = b
mx + y = 22
Please help! Thank you!!
This question is from textbook Beginning Algebra
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Find values for m and b in the following system so that the solution to the system is (-3,4)
They want you find both equations of a two-equation system
Find the 1st equation:
5x + 7y = b
:
Find b by using x,y coordinates given -3, 4
5(-3) + 7(4) = b
-15 + 28 = b
b = + 13
:
Find the slope (m): using y = mx + 13, using the given coordinates again
y = mx + b
4 = m(-3) + 13
4 = -3m + 13
3m = 13 - 4
3m = 9
m = +3
:
the 1st equation: y = 3x + 13; (m = +3 and b = +13)
:
:
Find the 2nd equation:
mx + y = 22
Find the slope (m) using the given coordinates x,y; -3,4
m(-3) + 4 = 22
-3m = 22 - 4
-3m = 18
m = 18/-3
m = -6
:
Find b in the 2nd equation, using the given coordinates for x & y again
y = mx + b
4 = -6(-3) + b
4 = 18 + b
4 -18 = b
b = -14
:
The 2nd equation: y = -6x - 14; (m =- 6 and b = -14)
:
If you graphed these two equations, you would find that they intersect at the given coordinates of -3,4
:
:
Did this make sense? Hope it did.
|
|
|
