Answer to Question #350887 in Algebra for diz

Question #350887

Instruction: Find the solution set of the following using 3 methods. Show your solutions, then submit your answer to your eLMS dropbox.





1.2x + y = 15



x - y = 9





2. 3x - 2y = 12



2x + 5y = 7


1
Expert's answer
2022-06-16T06:23:01-0400

There are three ways to solve systems of linear equations in two variables:

graphing.

substitution method.

elimination method.

1.



"2x + y = 15""x - y = 9"


a.


"(8, -1)"


b.



"2x + y = 15""x - y = 9"





"2x + x-9 = 15""y = x-9"





"3x = 24""y= x-9"





"x=8""y=-1"

"(8, -1)"


c.



"2x + y = 15""x - y = 9"





"3x - 2y = 12""2x + 5y = 72"





"2x + y+x-y= 15+9""x-y=9"





"3x = 24""x-y=9"





"x=8""8-y=9""x=8""y=-1"

"(8, -1)"


2.



"3x - 2y = 12""2x + 5y = 7"


a.



"(\\dfrac{74}{19}, -\\dfrac{3}{19})"


b.



"3x - 2y = 12""2x + 5y = 7"





"y = \\dfrac{3}{2}x-6""2x+5(\\dfrac{3}{2}x-6)=7"





"y = \\dfrac{3}{2}x-6""\\dfrac{19}{2}x=37"





"x=\\dfrac{74}{19}""y=\\dfrac{3}{2}(\\dfrac{74}{19})-6""x=\\dfrac{74}{19}""y=-\\dfrac{3}{19}"

"(\\dfrac{74}{19}, -\\dfrac{3}{19})"


c.



"3x - 2y = 12""2x + 5y = 7"





"6x - 4y = 24""6x + 15y = 21"





"6x+15y-(6x-4y)=21-24""3x-2y=12"





"19y=-3""x=\\dfrac{2}{3}y+4"





"x=\\dfrac{74}{19}""y=-\\dfrac{3}{19}"

"(\\dfrac{74}{19}, -\\dfrac{3}{19})"

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