Diophantine Equation | Number Theory | You should be able to solve this

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Diophantine Equation | Number Theory | You should be able to solve this

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After add the two equation
4x+3z= 15
We can take mod 3 both side
4x=0( mod 3)
X=0 ( mod 3)
X= 3a and a is an integer
3a>=0 a>=0

Sub x=3a in 4x+3z =15
We get z=5-4a>=0 a<=5/4
0<=a<=5/4
a is an integer a=0 or 1
If a= 0, x=0 and z=5
If a=1, x=3, z=1

And we can find y by subbing the value in any of two original equation

skwbusaidi
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Integers (x, y, z) (0, 0, 5) (3, 1, 3)

alinayfeh
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Request Calculus and Linear Algebra problems for College Students in Engineering and Science.

wira
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In this problem, it may be easier to double the second equation and subtract to not just cancel the z's, but the constant term as well. This yields 5x=3y. So x is a multiple of 3 and y is a multiple of 5.

dujas
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2:51 why can't decimal numbers be integers?

wira