How do you write a system of linear equations with only one solution? I know what the solution to the system is supposed to be, I just don't know how to go about writing the system for it.

Question

phi · Answer

write down the equation for two different lines
unless the lines are parallel the lines will meet.

the two equations represent a "system" of equations, and their intersection point is the solution.

mirandaregina · Answer

That makes sense to me, but how do I write the two equations when all the question tells us is that the solution needs to be (-1,4)?

phi · Answer

the solution (-1,4) means that point is on both lines.

the equation of a line in slope intercept form is
y= m x + b
if we put in -1 for x and 4 for y we have
4 = m*-1 + b
or
4=  -m + b

we need to pick a number for m and b.  It does not matter what they are...
I would keep things simple.  let b=0  so
4 = -m
and
m= -4  (multiply both sides by -1)

in other words,  one (of an infinite number of equations) that goes through (-1,4) is
y = -4x


now you find another equation.  Hint: you can't pick b=0 or you will get the same equation I did.

phi · Answer

for the second equation, pick a "nice" number for m, and then solve for b

mirandaregina · Answer

Okay, thank you! I'll use your directions and see what happens :)