Opalg said:[sp]
Multiply by $2$ and rearrange: $4xy - 6x - 10y = 2.$
Factorise: $(2x-5)(2y-3) = 17.$
Since $17$ is prime, there are just four possible cases:
1) $\quad 2x-5 = 17$, $2y-3 = 1$, giving $(x,y) = (11,2).$
2) $\quad 2x-5 = 1$, $2y-3 = 17$, giving $(x,y) = (3,10).$
3) $\quad 2x-5 = -17$, $2y-3 = -1$, giving $(x,y) = (-6,1).$
4) $\quad 2x-5 = -1$, $2y-3 = -17$, giving $(x,y) = (2,-7).$
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An integer equation is an equation where the only solutions are integers (whole numbers). This means that when solved, the values of the variables in the equation must be whole numbers, not fractions or decimals.
Unlike a regular equation, an integer equation has the additional constraint that the solutions must be integers. This makes it more challenging to solve, as the possible solutions are limited.
To solve an integer equation, you need to find values for the variables that make the equation true. This can be done through various methods such as substitution, elimination, or graphing. However, with integer equations, it is important to check that the solutions are integers before considering them as valid solutions.
Solving an integer equation can help us find the values of the variables that satisfy the given equation. This can be useful in real-life situations, such as in problem-solving and decision-making, where the values must be whole numbers.
No, there is no one-size-fits-all method for solving integer equations. The method used depends on the specific equation and its variables. Some equations may be easier to solve using one method while others may require a different approach.