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=152x + y = 15xy=9x - y = 9


a.


(8,1)(8, -1)


b.



2x+y=152x + y = 15xy=9x - y = 9





2x+x9=152x + x-9 = 15y=x9y = x-9





3x=243x = 24y=x9y= x-9





x=8x=8y=1y=-1

(8,1)(8, -1)


c.



2x+y=152x + y = 15xy=9x - y = 9





3x2y=123x - 2y = 122x+5y=722x + 5y = 72





2x+y+xy=15+92x + y+x-y= 15+9xy=9x-y=9





3x=243x = 24xy=9x-y=9





x=8x=88y=98-y=9x=8x=8y=1y=-1

(8,1)(8, -1)


2.



3x2y=123x - 2y = 122x+5y=72x + 5y = 7


a.



(7419,319)(\dfrac{74}{19}, -\dfrac{3}{19})


b.



3x2y=123x - 2y = 122x+5y=72x + 5y = 7





y=32x6y = \dfrac{3}{2}x-62x+5(32x6)=72x+5(\dfrac{3}{2}x-6)=7





y=32x6y = \dfrac{3}{2}x-6192x=37\dfrac{19}{2}x=37





x=7419x=\dfrac{74}{19}y=32(7419)6y=\dfrac{3}{2}(\dfrac{74}{19})-6x=7419x=\dfrac{74}{19}y=319y=-\dfrac{3}{19}

(7419,319)(\dfrac{74}{19}, -\dfrac{3}{19})


c.



3x2y=123x - 2y = 122x+5y=72x + 5y = 7





6x4y=246x - 4y = 246x+15y=216x + 15y = 21





6x+15y(6x4y)=21246x+15y-(6x-4y)=21-243x2y=123x-2y=12





19y=319y=-3x=23y+4x=\dfrac{2}{3}y+4





x=7419x=\dfrac{74}{19}y=319y=-\dfrac{3}{19}

(7419,319)(\dfrac{74}{19}, -\dfrac{3}{19})

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