SOLUTION: Explain how to apply elimination in solving a system of equations. a. Explain how to apply substitution in solving a system of equations. b. Demonstrate each technique in solvin

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Question 169709This question is from textbook elementary and Intermediate algebra concepts and application
: Explain how to apply elimination in solving a system of equations.
a. Explain how to apply substitution in solving a system of equations.
b. Demonstrate each technique in solving the system
3x + 9y = 12
5x - 4y = 3
This question is from textbook elementary and Intermediate algebra concepts and application

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Explain how to apply elimination in solving a system of equations.
a. Explain how to apply substitution in solving a system of equations.
b. Demonstrate each technique in solving the system
system%283x+%2B+9y+=+12%2C5x+-+4y+=+3%29

By elimination:

First eliminate x and find y.
Multiply the first equation through by -5 
and the second equation through by 3:

system%28-15x+-45y+=+-60%2C15x+-+12y+=+9%29

Now add vertically term by term:

-57y=-51

Divide both sides by -57

y=%28-51%29%2F%28-57%29

y=17%2F19

----

system%283x+%2B+9y+=+12%2C5x+-+4y+=+3%29

Next eliminate y and find x.
Multiply the first equation through by 
4 and the second equation through 
by 9:

system%2812x+%2B36y+=+48%2C45x+-+36y+=+27%29

Now add vertically term by term:

57x=75

Divide both sides by 57

x=75%2F57

x=25%2F19

Solution:   

-------------------

Now do the same problem from scratch using
substitution:

system%283x+%2B+9y+=+12%2C5x+-+4y+=+3%29

Solve the first equation for x:

3x+%2B+9y+=+12

Add -9x to both sides:

3x=12-9y

Divide through every term by 3:

%283x%29%2F3=12%2F3-%289y%29%2F3

Simplify:

x=4-3y

Substitute %284-3y%29 for x
in the second equation:

5x+-+4y+=+3%29
5%284-3y%29+-+4y+=+3%29
Distribute:
20-15y-4y=3
20-19y=3
Add -20 to both sides:
-19y=3-20
-19y=-17
Divide both sides by -19
%28-19y%29%2F%28-19%29=%28-17%29%2F%28-19%29
y=17%2F19

Now substitute %2817%2F19%29 for y
in

x=4-3y
x=4-3%2817%2F19%29
Write the 4 as 4%2F1 and 
write the 3 as 3%2F1

x=4%2F1-%283%2F1%29%2817%2F19%29
x=4%2F1-51%2F19

The LCD is 19
Multiply the 4%2F1 by 19%2F19

x=%284%2F1%29%2819%2F19%29-51%2F19
x=76%2F19-51%2F19
x=25%2F19

Solution:  

Edwin