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Question 825664: [ One number is greater by 6 than twice another number, but 3 times the smaller exceeds the greater by one. Find the numbers. ]
Is this the right formula?
Y= 2x + 6
3x + y= 1
I am not sure
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
it's important to define your variables right from the start.
doing so allows you to follow the logic of the problem statement, in clear mathematical form:
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x = smaller number
y = larger number
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y = 2x + 6
3x = y + 1
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now you have a proper linear system:
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put the system of linear equations into standard form:
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2x - y = -6
3x - y = 1
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copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = smaller number = 7
y = larger number = 20
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system matrix
2 -1
3 -1
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inverse of system matrix
-1 1
-3 2
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determinant of system matrix = 1
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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