What is the solution of 3x + y = 9 and 3x − 5y = 15?

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27-06-2018
Mathematics

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What is the solution of 3x + y = 9 and 3x − 5y = 15?

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puppies22 puppies22 · Answer 1 · 2018-06-27T21:11:45+02:00

So there are two ways.
First you could solve for y and plug it into the calculator. one equation for y1 and another for y2. Then go 2nd trace and press 5 and then press enter 3 times to find the intersection.
the second way is to solve by hand. I would suggest solve the first equation for y and plug the equation solved for y into the other equation. so y = -3x + 9 and 3x-5y=15. Then you could do 3x - 5(-3x+9) = 15. Finally solve for x and plug in x into both equations to see if you get the same y value.
The answer should be (10/3, -1)

mliguta mliguta · Answer 2 · 2018-06-27T21:26:35+02:00

[tex] \left \{{{3x+y=9} \atop {3x-5y=15}} \right. \\ \left \{ {{y=9-3x} \atop {3x-5(9-3x)=15}} \right. \\ \left \{ {{y=9-3x} \atop {3x-45+15x=15}} \right. \\ \left \{ {{y=9-3x} \atop {18x=60}} \right. \\ \left \{ {{y=9-3x} \atop {x= \frac{60}{18} }} \right. \\ \left \{ {{y=9-3x} \atop {x= \frac{10}{3} }} \right. \\ \left \{ {{y=9-3 \frac{10}{3} } \atop {x= \frac{10}{3} }} \right. \\ \left \{ {{y=-1} \atop {x= \frac{10}{3} }} \right. [/tex]