Question

How many solutions does this linear system have?

Answer 1

Answer:

The system of equations has no solution.

NO SOLUTION!

Step-by-step explanation:

Given the system of equations

$\begin{bmatrix}y=-\frac{1}{2}x+4\\ x+2y=-8\end{bmatrix}$

Arrange equation variables for elimination

$\begin{bmatrix}y+\frac{1}{2}x=4\\ 2y+x=-8\end{bmatrix}$

$\mathrm{Multiply\:}y+\frac{1}{2}x=4\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:2y+x=8$

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

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.

Answer 2

Answer:

No solution

Step-by-step explanation:

Got it right edge 2020