Can someone help me solve the following problems using the substituion method? I need to find the ordered pairs and I do not get it.... Here they are
1)
6m+n=47
m-4n=12
2)
6x+4y=-10
-7x+y=57
3)
5x+7y=43
-4x+y=25
I use substitution when I notice that in one of the equations one of the variables has a coefficient of 1
Then solve for that single variable
e.g. in #2
-7x + y = 57 ,
y = 7x + 57
now sub that into the other equation
6x + 4y = -10
6x + 4(7x+57) = 10
6x + 28x + 225 = 10
34x = - 218
x = -218/34 = - 109/17
then y = 7(-109/17) + 57
y = 206/17
do the other two the same way
Okay but the homework is saying the answer is (-7,8) so how would they have gotten that from the equation you did above?
I made a transcript error.
After 6x + 4(7x+57) = 10 it should have been
6x + 28x + 228 = -10
I had 2 errors in copying that line, sorry about that
Now i works out
Okay so what about number one it is a + and the a - for the second problem how do you figure a subtitution problem like that? do the signs make a difference?
For number 3 I got (6.7,51.8) is this correct?
Sure, I can help you solve these problems using the substitution method. Here's how you can do it:
1) To solve the system of equations:
6m + n = 47 --(1)
m - 4n = 12 --(2)
In equation (2), solve for m in terms of n:
m = 4n + 12
Substitute m in equation (1) with its value:
6(4n + 12) + n = 47
24n + 72 + n = 47
25n + 72 = 47
25n = 47 - 72
25n = -25
n = -1
Now, substitute the value of n in equation (2):
m - 4(-1) = 12
m + 4 = 12
m = 12 - 4
m = 8
So, the ordered pair (m, n) is (8, -1).
2) To solve the system of equations:
6x + 4y = -10 --(1)
-7x + y = 57 --(2)
In equation (2), solve for y in terms of x:
y = 57 + 7x
Substitute y in equation (1) with its value:
6x + 4(57 + 7x) = -10
6x + 228 + 28x = -10
34x + 228 = -10
34x = -10 - 228
34x = -238
x = -238/34
x = -7
Now, substitute the value of x in equation (2):
-7(-7) + y = 57
49 + y = 57
y = 57 - 49
y = 8
So, the ordered pair (x, y) is (-7, 8).
3) To solve the system of equations:
5x + 7y = 43 --(1)
-4x + y = 25 --(2)
In equation (2), solve for y in terms of x:
y = 25 + 4x
Substitute y in equation (1) with its value:
5x + 7(25 + 4x) = 43
5x + 175 + 28x = 43
33x + 175 = 43
33x = 43 - 175
33x = -132
x = -132/33
x = -4
Now, substitute the value of x in equation (2):
-4(-4) + y = 25
16 + y = 25
y = 25 - 16
y = 9
So, the ordered pair (x, y) is (-4, 9).
I hope this helps! Let me know if you have any further questions or need any more assistance.