SOLUTION: Question 1 : Show all work to solve this system by the substitution method : 4x + 2y = 6 6x = 9 - 3y a. What is the solution ? Show all work b. Is this system consis

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Question 1112052: Question 1 :
Show all work to solve this system by the substitution method :
4x + 2y = 6
6x = 9 - 3y
a. What is the solution ? Show all work
b. Is this system consistent or inconsistent ? Explain why.
c. Is this system dependent or independent ? Explain why.
Question 2 :
Given the system :
3x = 2y + 7
4x - 3y = 10
a. Solve this system using the Elimination/Addition Mehod : Put the equations in standard form. What variable did you eleminate first ? Show all work.
b. What is the solution ?
Question 3 :
There are three possibilities for the solution set of a system of linear equations. Describe each possibility, including if the system is consistent or inconsistent and if the system is dependent or independent and why. Explain what the graph of the equations for each possibility would look like.
Thank you very much

Found 2 solutions by ikleyn, stanbon:
Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website!
.
One and only one problem per post.

It is THE RULE of this forum.

When you violate this rule, you work AGAINST your better interests.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Question 1 :
Show all work to solve this system by the substitution method :
4x + 2y = 6
6x = 9 - 3y
a. What is the solution ? Show all work
2x + y = 3
2x + y = 3
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b. Is this system consistent or inconsistent ? Explain why.
consistent:: it has solutions--- an infinite number of them
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c. Is this system dependent or independent ? Explain why.
dependent:: one equation is a multiple of the other
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Question 2 :
Given the system :
3x = 2y + 7
4x - 3y = 10
a. Solve this system using the Elimination/Addition Mehod : Put the equations in standard form. What variable did you eleminate first ? Show all work.
12x - 8y = 28
12x - 9y = 30
---
y = -2
Solve for "x"::
x = (2y+7)/3 = (-4+7)/3 = 1
----
b. What is the solution ?::: (-2,1)
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Question 3 :
There are three possibilities for the solution set of a system of linear equations. Describe each possibility, including if the system is consistent or inconsistent and if the system is dependent or independent and why. Explain what the graph of the equations for each possibility would look like.
1st:: graphs intersect at one point:: consistent; independent
2nd:: graphs coincide at all points:: consistent; dependent
3rd:: graphs are parallel:: inconsistent; independent
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Cheers,
Stan H.
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