Question

Given that $x$ and $y$ are positive integers, possible solutions $(x,y)$ of the equation $3x+2y=11$ are:

• A. $(1,4)$
• B. $(3,1)$
• C. $(1,4)$ and $(2,2)$
• D. $(1,4)$ and $(3,1)$
• E. $(2,2)$ and $(3,1)$

Answer 1

Answer: (D)

$(1,4)$ and $(3,1)$

If $3x+2y=11$
then $x$ must be odd in order for the final solution to be $11$ so $x$ can be $1$ or $3$ because those are the only odd values for $x$ that stay under $11$ when multiplied by $3$.

Substitute $x$ to be $1$ or $3$ you then solve for $y$
for $x=1$,

$3\left(1\right)+2y=11$
$2y=8$
$y=4$
for $x=3$,

$3\left(3\right)+2y=11$
$2y=2$
$y=1$
Therefore, there are 2 solutions for $3x+2y=11$ where $x$ is a positive integer are $(1,4)$ and $(3,1)$.