SOLUTION: 26. 10m-9n=15 27. 3c-7d= -3 28. 6g-8h=50 30. 3x= -31+2y
5m-4n=10 2c+6d= -34 4g+6h=22 5x+6y=23
Algebra.Com
Question 128354This question is from textbook
: 26. 10m-9n=15 27. 3c-7d= -3 28. 6g-8h=50 30. 3x= -31+2y
5m-4n=10 2c+6d= -34 4g+6h=22 5x+6y=23
This question is from textbook
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started
Start with the given system of equations:
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for n.
So let's isolate n in the first equation
Start with the first equation
Subtract from both sides
Rearrange the equation
Divide both sides by
Break up the fraction
Reduce
---------------------
Since , we can now replace each in the second equation with to solve for
Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
Distribute to
Multiply
Multiply both sides by the LCM of 9. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)
Distribute and multiply the LCM to each side
Combine like terms on the left side
Subtract 60 from both sides
Combine like terms on the right side
Divide both sides by 5 to isolate m
Divide
-----------------First Answer------------------------------
So the first part of our answer is:
Since we know that we can plug it into the equation (remember we previously solved for in the first equation).
Start with the equation where was previously isolated.
Plug in
Multiply
Combine like terms and reduce. (note: if you need help with fractions, check out this solver)
-----------------Second Answer------------------------------
So the second part of our answer is:
-----------------Summary------------------------------
So our answers are:
and
# 27
Start with the given system of equations:
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for d.
So let's isolate d in the first equation
Start with the first equation
Subtract from both sides
Rearrange the equation
Divide both sides by
Break up the fraction
Reduce
---------------------
Since , we can now replace each in the second equation with to solve for
Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
Distribute to
Multiply
Multiply both sides by the LCM of 7. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)
Distribute and multiply the LCM to each side
Combine like terms on the left side
Subtract 18 from both sides
Combine like terms on the right side
Divide both sides by 32 to isolate c
Divide
-----------------First Answer------------------------------
So the first part of our answer is:
Since we know that we can plug it into the equation (remember we previously solved for in the first equation).
Start with the equation where was previously isolated.
Plug in
Multiply
Combine like terms and reduce. (note: if you need help with fractions, check out this solver)
-----------------Second Answer------------------------------
So the second part of our answer is:
-----------------Summary------------------------------
So our answers are:
and
RELATED QUESTIONS
What are the answers to all of these questions?
1. -6k+7k 2. 12r-8-12
3.... (answered by Fombitz)
6n+4n-n+5=23
36-4c-3c=22
28=10a-5a-2
3/8+p/8-31/8
4g/14-3/7-g/14=3/14... (answered by checkley77)
6.1
I. Solve each system by graphing, and classify the system as dependent or... (answered by Flake)
Construct a grouped frequency distribution for the following 28 scores using a class... (answered by jim_thompson5910)
6y-3g+2y-4g
4u-7y+11u-5y
5x-7y+3x-4y
12b-4c+3b-2c
6r-5t-8r-4t
(answered by AnlytcPhil)
The positive integers are arranged in the pattern illustrated below:
1 2 5 10 17 26
3 (answered by greenestamps)
3 pts) Given U = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}, A = {21, 23, 25, 27, 29},... (answered by dyakobovitch)
what is the sequence of this (2, 3, 4, 5, 7, 8 ,9, 10, 11, 13, 14, 15, 16 ,17, 19, 21,... (answered by richard1234)
I need help solving this problem:
Express in simplest radical form:
1. √8 2.... (answered by Alan3354)