Question

Find three points with integer valued coordinates that solve the equation -2x-3y=-7

Answer 1

(-1, 3), (2, 1), (5, -1)

Explanation:

We have the equation of the line in the standard form:

`Ax+By=C`

Convert to the slope-intercept form:

`y=mx+b`

`-2x-3y=-7` add 2x to both sides

`-3y=2x-7` divide both sides by (-3)

`y=-(2)/(3)x+(7)/(3)`

for x = -1

`y=-(2)/(3)(-1)+(7)/(3)=(2)/(3)+(7)/(3)=(2+7)/(3)=(9)/(3)=3\to(-1,\ 3)`

for x = 2

`y=-(2)/(3)(2)+(7)/(3)=-(4)/(2)+(7)/(3)=(-4+7)/(3)=(3)/(3)=1\to(2,\ 1)`

for x = 5

`y=-(2)/(3)(5)+(7)/(3)=-(10)/(3)+(7)/(3)=(-10+7)/(3)=(-3)/(3)=-1\to(5,\ -1)`