Question 1056866: Solve the following system of linear equation using any
algebraic method,and if possible show solution check.
2x-5y=3
x-2y=7
Thank you very much,
Anneliese
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website!
2x-5y = 3
x-2y = 7
Solve the 2nd equation for x
x-2y = 7
x = 7+2y
Substitute (7+2y) for x in the 1st equation:
2x-5y = 3
2(7+2y)-5y = 3
14+4y-5y = 3
14-y = 3
-y = -11
y = 11
Substitute (11) for y in
x = 7+2y
x = 7+2(11)
x = 7+22
x = 29
Solution (x,y) = (29,11)
To check, substitute (11) for x and (29) for y
in BOTH of the original equations:
Substituting in the first one:
2x-5y = 3
2(29)-5(11) = 3
58-55 = 3
3 = 3
That checks. But we must check the solution in
the other equation to show that it checks in both:
x-2y = 7
(29)-2(11) = 7
29 - 22 = 7
7 = 7
That checks too. Therefore we now know that
(x,y) = (29,11) is the correct solution.
Edwin
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