Question

Y=-6x+2

How many solutions does this linear system have?
O one solution: (0, 0)
Oone solution: (1, 4)
O no solution
Oinfinite number of Solutions
-12x– 2y =4

Answer 1

The system has of the equation has no solution

Thus,

NO SOLUTION!

Explanation:

Given the system of equations

`\begin{bmatrix}y=-6x+2\\ -12x-2y=4\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}y+6x=2\\ -2y-12x=4\end{bmatrix}`

`\mathrm{Multiply\:}y+6x=2\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:2y+12x=4`

so

`\begin{bmatrix}2y+12x=4\\ -2y-12x=4\end{bmatrix}`

adding both equations

`-2y-12x=4`

`+`

`\underline{2y+12x=4}`

`0=8`

so

`\begin{bmatrix}2y+12x=4\\ 0=8\end{bmatrix}`

0 = 8 is false, therefore the system has of the equation has no solution

Thus,

NO SOLUTION!

Please also check the attached figure.