Question

How many solutions does the system have? You can use the interactive graph below to find the answer. 4x-2y=8 2x+y=2 4x−2y=8 2x+y=2 ​ A.One solution B.two solutions. C.Many solutions

Answer 1

Answer:

Step-by-step explanation:

We have the following system

$\left[\begin{matrix} 4 & -2 \\ 2 & 1 \end{matrix}\right]x =\left[\begin{matrix} 8 \\ 2 \end{matrix}\right]$

The number of solutions depend on the determinant of the matrix of the system. If the determinant is different from 0, then it has one unique solution, if it 0 then it has infinite solutions.

Note that the determinant of a matrix

$\left[\begin{matrix} a & b \\ c & d \end{matrix}\right]$ is ad-bc. So in our case we have 4*1-(-2)*2 = 8  which is not 0. Then the system has an unique solution.