Question

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.

Answer 1

I hope this helps you



1)



x= -2y


2. (-2y)+4y=0


0=0


2)


x+2x= -3


x=-1


y= -2


3)


7x+2x+2=4



9x=2


x=2/9


y=2/9+1


y=11/9

Answer 2

1.
x + 2y = 0
2x + 4y = 0

Coincident

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2.
y = 2x
x + y = -3
⇒ x + 2x = -3
⇒ x = -1
⇒ y = -2
Solution is (-1, -2)
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3.
y = x + 1

7x + 2y = 4
⇒ 7x + 2x +2 = 4
⇒ 9x = 2
⇒ x = 2/9
y = 1+ x = 11/9

Solution is (2/9, 11/9)

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Hope it helps!