What are all tuples off postive integers w,x,y,z that fullfill following system of equations:
$$ x + 10z^2 = 2014 $$ $$ 2y + z = 54$$ $$ (y+2x + \frac{7}{2}w)z=1211$$
I am really lost - all my attemps lead into disaster..
2026-03-28 14:25:56.1774707956
How to find all positive integer solutions of this tricky system of equations?
131 Views Asked by user161516 https://math.techqa.club/user/user161516/detail At
1
There are 1 best solutions below
Related Questions in SYSTEMS-OF-EQUATIONS
- Can we find $n$ Pythagorean triples with a common leg for any $n$?
- System of equations with different exponents
- Is the calculated solution, if it exists, unique?
- System of simultaneous equations involving integral part (floor)
- Solving a system of two polynomial equations
- Find all possible solution in Z5 with linear system
- How might we express a second order PDE as a system of first order PDE's?
- Constructing tangent spheres with centers located on vertices of an irregular tetrahedron
- Solve an equation with binary rotation and xor
- Existence of unique limit cycle for $r'=r(μ-r^2), \space θ' = ρ(r^2)$
Related Questions in INTEGERS
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Which sets of base 10 digits have the property that, for every $n$, there is a $n$-digit number made up of these digits that is divisible by $5^n$?
- Ring of remainders definition
- Proof of well-ordering property
- Compute a division with integer and fractional part
- Solving for 4 variables using only 2 equations
- For any natural numbers a, b, c, d if a*b = c*d is it possible that a + b + c + d is prime number
- Can I say this :$e^{{(294204)}^{1/11}}-{(294204)}^{1/11}$ integer number or almost integer?
- Pack two fractional values into a single integer while preserving a total order
- What will be the difference?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
One approach is to use basic detective work. From the second equation, $z$ is even. Now look at the first equation $x+10z^2=2014$. Since $z$ is even and positive, there are not many possibilities for $z$. For already at $z=20$ we have $10z^2$ is quite a bit bigger than $2014$.
So there are not many cases to check. A bit grungy, but you will soon arrive at the solution.
By the way, $1211=(7)(173)$. If you think about this, you will arrive at the answer in one step.