SOLUTION: Solve this system: 3x - 2y = 23 x + 5y = -15

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Question 176579: Solve this system:
3x - 2y = 23
x + 5y = -15
Found 2 solutions by jojo14344, MathLover1:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

3x+-+2y+=+23+, EQN 1
x+%2B+5y+=+-15+, EQN 2
In EQN 2 we get,
5y=-15-x---->cross%285%29y%2Fcross%285%29=%28-15-x%29%2F5
y=%28-15%2F5%29-%28x%2F5%29
y=-3-%281%2F5%29x, EQN 3, subst in EQN 1:
3x-2%28-3-%281%2F5%29x%29=23
3x%2B6%2B%282%2F5%29x=23
%2815x%2B2x%29%2F5=23-6
17x%2F5=17---->17x=5%2A17---->cross%2817%29x%2Fcross%2817%29=5%2Across%2817%29%2Fcross%2817%29
highlight%28x=5%29, subst in EQN 3:
y=-3-%281%2F5%29%285%29=-3-1
highlight%28y=-4%29
See graph:
-----> RED>>> EQN 2; GREEN>>> EQN 1
thank you,
Jojo

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


3x-2y=23

1x%2B5y=-15





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


3x-2y=23 Start with the given equation



-2y=23-3x Subtract 3+x from both sides



-2y=-3x%2B23 Rearrange the equation



y=%28-3x%2B23%29%2F%28-2%29 Divide both sides by -2



y=%28-3%2F-2%29x%2B%2823%29%2F%28-2%29 Break up the fraction



y=%283%2F2%29x-23%2F2 Reduce



Now lets graph y=%283%2F2%29x-23%2F2 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F2%29x-23%2F2%29+ Graph of y=%283%2F2%29x-23%2F2




So let's solve for y on the second equation


1x%2B5y=-15 Start with the given equation



5y=-15-x Subtract +x from both sides



5y=-x-15 Rearrange the equation



y=%28-x-15%29%2F%285%29 Divide both sides by 5



y=%28-1%2F5%29x%2B%28-15%29%2F%285%29 Break up the fraction



y=%28-1%2F5%29x-3 Reduce





Now lets add the graph of y=%28-1%2F5%29x-3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F2%29x-23%2F2%2C%28-1%2F5%29x-3%29+ Graph of y=%283%2F2%29x-23%2F2(red) and y=%28-1%2F5%29x-3(green)


From the graph, we can see that the two lines intersect at the point (5,-4) (note: you might have to adjust the window to see the intersection)