Question

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

Answer 1

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:

• y = 0
• x = 2

Therefore, the correct option is C.

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