I need help rq what is the x-coordinate of the solution to the following system of equations? x - 2y = 2 3x + y = 6 a) x= -2 b) x=0 c) x= 2 d) x= 3

Question

asked Aug 11, 2023 74.0k views

1 Answer

Nigel Harper · Answer 1 · 2023-08-17T15:29:07+0000

We have the system of equations:

x - 2y = 2

3x + y = 6

From equation 1 we express y.

x - 2y = 2

We pass the addend with the variable x from the left to the right and change the sign.

-2y = 2 - x

We divide both parts of the equation by the multiplier of y.

((-1)2y)/(-2)=(2-x)/(-2)

y=(x)/(2)-1

We put the result y in equation 2.

3x + y = 6

We obtain:

$3x+\left((x)/(2)-1\right)=6$

(7x)/(2)-1=6

We pass the free addend -1 from the left to the right, changing the sign.

(7x)/(2)=1+6

(7x)/(2)=2

We divide both parts of the equation by the multiplier of x.

((7)/(2)x )/((7)/(2) )=(7)/((7)/(2))

x=2

What

y=(x)/(2)-1

then

$y=-1+(1)/(2)\cdot2$

y=0

Answer:

Therefore, the correct option is C.

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