Question 1007035
Assume that *[tex \large (x_0, y_0)] is a solution to the system


*[tex \large a_1 x + a_2 y = c_1]
*[tex \large b_1 x + b_2 y = c_2]

Then all that needs to be done is show that *[tex \large (x_0, y_0)] is a solution to the system


*[tex \large a_1 x + a_2 y = c_1]
*[tex \large (a_1 + kb_1)x + (a_2 + kb_2)y = c_1 + kc_2] (for some constant k)


Note that the second equation was formed by taking the first and adding k times the second. However this pretty easily holds true from linearity as the second equation is equivalent to


*[tex \large (a_1x + a_2y) + k(b_1x + b_2y) = c_1 + kc_2]


which is true.