Mathematics: 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

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How many solutions does this linear system have?

tiffanybrown703

13.02.2022

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.

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