Determine which of the following ordered pairs is a solution to the equation 3x−8=−4y

Question

.(1 point)
Responses

(1,1)
left parenthesis 1 comma 1 right parenthesis

(0,2)
left parenthesis 0 comma 2 right parenthesis

(−1,1)
left parenthesis negative 1 comma 1 right parenthesis

(0,−2)

Answer 1

To determine which of the ordered pairs is a solution to the equation $3x-8=-4y$, we will substitute the $x$ and $y$ values from each ordered pair into the equation and see if the equation holds true.

1. For the pair $(1,1)$: $$3(1)-8=-4(1)$$ $$3-8=-4$$ $$-5\ne -4(\text{Not a solution})$$

2. For the pair $(0,2)$: $$3(0)-8=-4(2)$$ $$-8=-8(\text{This is a solution})$$

3. For the pair $(-1,1)$: $$3(-1)-8=-4(1)$$ $$-3-8=-4$$ $$-11\ne -4(\text{Not a solution})$$

4. For the pair $(0,-2)$: $$3(0)-8=-4(-2)$$ $$-8=8(\text{Not a solution})$$

After checking all ordered pairs, we find that the only solution is:

(0, 2).