SOLUTION: Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions as the one shown.
8x + 7y = 39
4x –
Algebra.Com
Question 1007035: Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions as the one shown.
8x + 7y = 39
4x – 14y = –68
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Assume that )
is a solution to the system
Then all that needs to be done is show that is a solution to the system
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
 + k(b_1x + b_2y) = c_1 + kc_2)
which is true.
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