Question

2x + 3y = -12
select all answers that apply:
a (0, -4)
b (2, -1)
c (0,0)
d (-6,0)

Answer 1

To determine which of the given points satisfy the equation \(2x + 3y = -12\), we can plug in the coordinates of each point into the equation and see if it holds true.

1. **Point a: (0, -4)**
Substitute \(x = 0\) and \(y = -4\):
\[
2(0) + 3(-4) = 0 - 12 = -12 \quad \text{(True)}
\]

2. **Point b: (2, -1)**
Substitute \(x = 2\) and \(y = -1\):
\[
2(2) + 3(-1) = 4 - 3 = 1 \quad \text{(False)}
\]

3. **Point c: (0, 0)**
Substitute \(x = 0\) and \(y = 0\):
\[
2(0) + 3(0) = 0 \quad \text{(False)}
\]

4. **Point d: (-6, 0)**
Substitute \(x = -6\) and \(y = 0\):
\[
2(-6) + 3(0) = -12 + 0 = -12 \quad \text{(True)}
\]

The points that satisfy the equation \(2x + 3y = -12\) are:
- (0, -4) (option a)
- (-6, 0) (option d)

So, the answers that apply are **a and d**.