Question

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

Answer 1

SOLUTION

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

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

Set y = 0

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

Set y = 1

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

Hence, the three different solutions are:

$\begin{gathered} (0,3) \\ (-4,0) \\ (-\frac{8}{3},1) \end{gathered}$