Respuesta :
Answer:
There are infinitely many solutions
Explanation:
Given the system of linear equations:
[tex]\mleft\{\begin{aligned}6x-30y=18 \\ 5x+25y=15\end{aligned}\mright.[/tex]To solve using Matrices, we write the equation in the form:
Ax = b
Where A represent the matrix of the coefficient of the variables x and y
x represent the matrix of the variables x and y
and b represents the matrix of the constants on the right hand side.
In matrix form, we have:
[tex]\begin{bmatrix}{6} & {-30} \\ {5} & {-25}\end{bmatrix}\begin{bmatrix}{x} \\ {y}\end{bmatrix}=\begin{bmatrix}{18} \\ {15}\end{bmatrix}[/tex]We must have a nonzero determinant for A
The determinant of A is:
[tex]\begin{gathered} (-25\times6)-(-30\times5) \\ =-150+150 \\ =0 \end{gathered}[/tex]The determinant of A is zero, without going far, we conclude that the system has infinite number of solutions.
