Problem $9.$ In this problem, do not do any row operations or solve any system of linear equations; instead, use your knowledge of vector spaces. Knowing that the linear system

$5x_1+x_2-3x_3=0$

$-9x_1+2x_2+5x_3=1$

$4x_1+x_2-6x_3=9$

is consistent, explain why the linear system

$5x_1+x_2-3x_3=0$

$-9x_1+2x_2+5x_3=5$

$4x_1+x_2-6x_3=45$

must also be consistent.