SOLUTION: Solve 3x+2y=-6 -2x+5y=23 and classify the system

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Question 173315This question is from textbook Saxon Algebra 2
: Solve
3x+2y=-6
-2x+5y=23
and classify the system This question is from textbook Saxon Algebra 2

Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%283x%2B2y=-6%2C-2x%2B5y=23%29


2%283x%2B2y%29=2%28-6%29 Multiply the both sides of the first equation by 2.


6x%2B4y=-12 Distribute and multiply.


3%28-2x%2B5y%29=3%2823%29 Multiply the both sides of the second equation by 3.


-6x%2B15y=69 Distribute and multiply.


So we have the new system of equations:
system%286x%2B4y=-12%2C-6x%2B15y=69%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:


%286x%2B4y%29%2B%28-6x%2B15y%29=%28-12%29%2B%2869%29


%286x%2B-6x%29%2B%284y%2B15y%29=-12%2B69 Group like terms.


0x%2B19y=57 Combine like terms. Notice how the x terms cancel out.


19y=57 Simplify.


y=%2857%29%2F%2819%29 Divide both sides by 19 to isolate y.


y=3 Reduce.


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


6x%2B4y=-12 Now go back to the first equation.


6x%2B4%283%29=-12 Plug in y=3.


6x%2B12=-12 Multiply.


6x=-12-12 Subtract 12 from both sides.


6x=-24 Combine like terms on the right side.


x=%28-24%29%2F%286%29 Divide both sides by 6 to isolate x.


x=-4 Reduce.


So our answer is x=-4 and y=3.


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%2B2y=-6 (red) and -2x%2B5y=23 (green)

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
3x+2y=-6....eq 1
-2x+5y=23....eq 2
lets use the process of elimination which means we need to manipulate eq 1 and 2 such that one of the variables is eliminated. There are various numbers we could multiply by the equations to reach this objective. Lets multiply eq 1 by 5 and eq 2 by -2 so that the y terms will be eliminated
:
15x+10y=-30...revised eq 1
4x-10y=-46....revised eq 2
:
now observing the equations we can see that when the equations are added to one another that the y terms are eliminated 10y-10y=0. We are left with
15x+4x=-30-46
:
19x=-76
:
highlight%28x=-4%29
:
now we take x's found value and plug it back into any equation to find y's value. I choose eq 1
:
3(-4)+2y=-6
:
-12+2y=-6
:
2y=6
:
highlight%28y=3%29