SOLUTION: Think i did them right but 2 & 3 are I get no solution and want to make sure I am not leaving something out. 1. Solve by substitution or elimination method: 3x

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Question 185456: Think i did them right but 2 & 3 are I get no solution and want to make sure I am not leaving something out.
1. Solve by substitution or elimination method:
3x – 2y = 26
-7x + 3y = -49
2. Solve by substitution or elimination method:
4x – 5y = 14
-12x + 15y = -42
3. Solve by substitution or elimination method:
-2x + 6y = 19
10x – 30y = -15
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

Let's solve this system by elimination



Start with the given system of equations:
system%283x-2y=26%2C-7x%2B3y=-49%29


3%283x-2y%29=3%2826%29 Multiply the both sides of the first equation by 3.


9x-6y=78 Distribute and multiply.


2%28-7x%2B3y%29=2%28-49%29 Multiply the both sides of the second equation by 2.


-14x%2B6y=-98 Distribute and multiply.


So we have the new system of equations:
system%289x-6y=78%2C-14x%2B6y=-98%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%289x-6y%29%2B%28-14x%2B6y%29=%2878%29%2B%28-98%29


%289x%2B-14x%29%2B%28-6y%2B6y%29=78%2B-98 Group like terms.


-5x%2B0y=-20 Combine like terms.


-5x=-20 Simplify.


x=%28-20%29%2F%28-5%29 Divide both sides by -5 to isolate x.


x=4 Reduce.


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


9x-6y=78 Now go back to the first equation.


9%284%29-6y=78 Plug in x=4.


36-6y=78 Multiply.


-6y=78-36 Subtract 36 from both sides.


-6y=42 Combine like terms on the right side.


y=%2842%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=-7 Reduce.


So the solutions are x=4 and y=-7.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 3x-2y=26 (red) and -7x%2B3y=-49 (green)


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# 2


Let's solve this system by elimination


Start with the given system of equations:
system%284x-5y=14%2C-12x%2B15y=-42%29


3%284x-5y%29=3%2814%29 Multiply the both sides of the first equation by 3.


12x-15y=42 Distribute and multiply.


So we have the new system of equations:
system%2812x-15y=42%2C-12x%2B15y=-42%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%2812x-15y%29%2B%28-12x%2B15y%29=%2842%29%2B%28-42%29


%2812x%2B-12x%29%2B%28-15y%2B15y%29=42%2B-42 Group like terms.


0x%2B0y=0 Combine like terms.


0=0Simplify.


Since 0=0 is always true, this means that there are an infinite number of solutions.


So the system is consistent and dependent.


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# 3




Start with the given system of equations:
system%28-2x%2B6y=19%2C10x-30y=-15%29


5%28-2x%2B6y%29=5%2819%29 Multiply the both sides of the first equation by 5.


-10x%2B30y=95 Distribute and multiply.


So we have the new system of equations:
system%28-10x%2B30y=95%2C10x-30y=-15%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-10x%2B30y%29%2B%2810x-30y%29=%2895%29%2B%28-15%29


%28-10x%2B10x%29%2B%2830y%2B-30y%29=95%2B-15 Group like terms.


0x%2B0y=80 Combine like terms.


0=80Simplify.


Since 0=80 is never true, this means that there are no solutions.


So the system is inconsistent.