Question

Given the equation 2x = 4y - 3 write another linear equation that would create a system that has the number of solutions listed

A . 0 Solutions
B . 1 Solution
C . Infinitely many solutions

Answer 1

A.
`2x-4y=\pi`
B.
`x=1`

C.
`2x-4y=3`

Explanation:

A.
`2x-4y=\pi`. Any number could work as long as the coefficients for x and y stays the same. You are basically imposing that the quantity 2x-4y (if you bring 4y to the LHS) is equal to both -3 AND
`\pi`, or any number you like. But yesterday was 3/14 so let's pick a fun number!

B.
`x=1` Or
`y=1`. Or as long as you don't pick the same ratios of x and y you're golden. But x=1 is the easiest that comes to mind

C.
`2x-4y=3`. To get infinitely many solutions you just have to rewrite the equation again. Maybe move things around if you prefer, or multiply everything by a number you lile.