Question

For each ordered pair, determine whether it is a solution to 6x + 7y = 19.
(0, -3)
(3, -4)
(-5, 7)
(2, 1)

Answer 1

To determine whether each ordered pair \((x, y)\) is a solution to the equation \(6x + 7y = 19\), we will substitute the \(x\) and \(y\) values from each pair into the equation and see if the equation holds true.

1. For the pair \((0, -3)\):
\[
6(0) + 7(-3) = 0 - 21 = -21 \quad \text{(not equal to 19)}
\]

2. For the pair \((3, -4)\):
\[
6(3) + 7(-4) = 18 - 28 = -10 \quad \text{(not equal to 19)}
\]

3. For the pair \((-5, 7)\):
\[
6(-5) + 7(7) = -30 + 49 = 19 \quad \text{(equal to 19)}
\]

4. For the pair \((2, 1)\):
\[
6(2) + 7(1) = 12 + 7 = 19 \quad \text{(equal to 19)}
\]

Now, summarizing the results:
- \((0, -3)\) is **not** a solution.
- \((3, -4)\) is **not** a solution.
- \((-5, 7)\) **is** a solution.
- \((2, 1)\) **is** a solution.