Question

Find three different solutions for the equation 3x-4y=-12

Answer 1

Given the question, the following are the solution steps to answer the question.

STEP 1: Write the given equation.

`3x-4y=-12`

STEP 2: Find the solutions

`3x-4y=-12`

Set x = 0

`\begin{gathered} 3(0)-4y=-12 \\ -4y=-12 \\ y=(-12)/(-4)=3 \\ Solution:(0,3) \end{gathered}`

Set y = 0

`\begin{gathered} 3x-4(0)=-12 \\ 3x-0=-12 \\ 3x=-12 \\ Divide\text{ both sides by 3} \\ (3x)/(3)=(-12)/(3) \\ x=-4 \\ Solution:(-4,0) \end{gathered}`

Set y = 1

`\begin{gathered} 3x-4(1)=-12 \\ 3x-4=-12 \\ 3x=-12+4 \\ 3x=-8 \\ Divide\text{ both sides by 3} \\ (3x)/(3)=(-8)/(3) \\ x=-(8)/(3) \\ Solution:(-(8)/(3),1) \end{gathered}`

Hence, the three different solutions are:

`\begin{gathered} (0,3) \\ (-4,0) \\ (-(8)/(3),1) \end{gathered}`