Question

How many solutions does this linear system have?

y=-1/2x+4
one solution: (8, 0)
one solution: (0, 8)
no solution
infinite number of solutions

Answer 1

No solution

Explanation:

Got it right edge 2020

Answer 2

The system of equations has no solution.

NO SOLUTION!

Explanation:

Given the system of equations

`\begin{bmatrix}y=-(1)/(2)x+4\\ x+2y=-8\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}y+(1)/(2)x=4\\ 2y+x=-8\end{bmatrix}`

`\mathrm{Multiply\:}y+(1)/(2)x=4\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:2y+x=8`

`\begin{bmatrix}2y+x=8\\ 2y+x=-8\end{bmatrix}`

subtracting equation 2y+x=8 from 2y+x = -8

`2y+x=-8`

`-`

`\underline{2y+x=8}`

`0=-16`

so the equations become

`\begin{bmatrix}2y+x=8\\ 0=-16\end{bmatrix}`

0 = -16 is false, therefore the system of equations has no solution.

NO SOLUTION!

The diagram is also attached below.