SOLUTION: How do you solve this system of equations using substitution (not elimination): 5x - 9y = 11 and 3x + 7y = 19. Please show me the step-by-step solution, as I would appreciate this

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: How do you solve this system of equations using substitution (not elimination): 5x - 9y = 11 and 3x + 7y = 19. Please show me the step-by-step solution, as I would appreciate this       Log On


   

Question 684766: How do you solve this system of equations using substitution (not elimination): 5x - 9y = 11 and 3x + 7y = 19. Please show me the step-by-step solution, as I would appreciate this very much. I tried doing this problem numerous times, but my solutions didn't make sense. I have a test soon, and I am worried I'll not be prepared.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Solve one the equations for x or y, then substitute that equation into the other for that variable.
...
5x - 9y = 11
5x = 11 + 9y
x = 11%2F5+%2B+%289%2F5%29y
...
3x + 7y = 19 ==> substitution
3(11%2F5+%2B+%289%2F5%29y) + 7y = 19 ==> distriubte the 3
33%2F5+%2B+%2827%2F5%29y + 7y = 19 ==> combine like terms
%2833%2F5%29+%2B+%2827%2F5%29y+%2B+7%285%2F5%29y+=+19
%2833%2F5%29+%2B+%2827%2F5%29y+%2B+%2835%2F5%29y+=+19
%2833%2F5%29+%2B+%2862%2F5%29y+=+19 ==> isolate the y variable
%2862%2F5%29y+=+19+-+%2833%2F5%29
...
%2862%2F5%29y+=+19%285%2F5%29+-+%2833%2F5%29
%2862%2F5%29y+=+95%2F5+-+33%2F5
%2862%2F5%29y+=+62%2F5 ==> multiply both sides by 5%2F62
y = 1
...
Plug the y variable into the equation to solve for x
x = 11%2F5+%2B+9%2F5+=+20%2F5+=+4
...
x = 4, y = 1
(4, 1) is the solution
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