Question

Are these ordered pairs in the solution set of y = 2x + 1?

(3,7)
(-1/2,0)
(0,1)
(2,6)

Answer 1

To determine if the ordered pairs are in the solution set of the equation \( y = 2x + 1 \), we need to substitute the \( x \) value from each pair into the equation and see if the resulting \( y \) value matches the \( y \) value in the ordered pair.

1. For the pair \( (3, 7) \):
- Substitute \( x = 3 \):
\[
y = 2(3) + 1 = 6 + 1 = 7
\]
- The ordered pair \( (3, 7) \) is in the solution set.

2. For the pair \( (-\frac{1}{2}, 0) \):
- Substitute \( x = -\frac{1}{2} \):
\[
y = 2\left(-\frac{1}{2}\right) + 1 = -1 + 1 = 0
\]
- The ordered pair \( \left(-\frac{1}{2}, 0\right) \) is in the solution set.

3. For the pair \( (0, 1) \):
- Substitute \( x = 0 \):
\[
y = 2(0) + 1 = 0 + 1 = 1
\]
- The ordered pair \( (0, 1) \) is in the solution set.

4. For the pair \( (2, 6) \):
- Substitute \( x = 2 \):
\[
y = 2(2) + 1 = 4 + 1 = 5
\]
- The ordered pair \( (2, 6) \) is not in the solution set, since \( 6 \neq 5 \).

In summary, the following ordered pairs are in the solution set of \( y = 2x + 1 \):
- \( (3, 7) \)
- \( \left(-\frac{1}{2}, 0\right) \)
- \( (0, 1) \)

The ordered pair \( (2, 6) \) is NOT in the solution set.