SOLUTION: 2x+5y=4 x+5y=7

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Question 178815: 2x+5y=4
x+5y=7
Found 2 solutions by jim_thompson5910, jojo14344:
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%282x%2B5y=4%2Cx%2B5y=7%29


-1%28x%2B5y%29=-1%287%29 Multiply the both sides of the second equation by -1.


-1x-5y=-7 Distribute and multiply.


So we have the new system of equations:
system%282x%2B5y=4%2C-1x-5y=-7%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:


%282x%2B5y%29%2B%28-1x-5y%29=%284%29%2B%28-7%29


%282x%2B-1x%29%2B%285y%2B-5y%29=4%2B-7 Group like terms.


x%2B0y=-3 Combine like terms.


x=-3 Simplify.


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


2x%2B5y=4 Now go back to the first equation.


2%28-3%29%2B5y=4 Plug in x=-3.


-6%2B5y=4 Multiply.


5y=4%2B6 Add 6 to both sides.


5y=10 Combine like terms on the right side.


y=%2810%29%2F%285%29 Divide both sides by 5 to isolate y.


y=2 Reduce.


So our answer is x=-3 and y=2.


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 2x%2B5y=4 (red) and x%2B5y=7 (green)

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

Line eqns:system%282x%2B5y=4%28EQN1%29%2Cx%2B5y=7%28EQN2%29%29
In EQN 2 we get,
5y=7-x--->cross%285%29y%2Fcross%285%29=%287-x%29%2F5
y=7%2F5-%281%2F5%29x, EQN 3,subst. in EQN 1:
2x%2B5%287%2F5-%281%2F5%29x%29=4---->2x%2Bcross%285%29%2A%287%2Fcross%285%29%29-cross%285%29%2A%281%2Fcross%285%29%29x=4
2x%2B7-x=4
x=4-7=highlight%28-3=x%29 subst. in EQN 3:
y=7%2F5-%281%2F5%29%28-3%29=7%2F5%2B3%2F5=10%2F5
highlight%28y=2%29
As we see the graph,
----->RED>>> EQN 1; GREEN EQN 2
Thank you,
Jojo