Question

A system of equations has the solution (6, 2).

What could the other equation be?

y = - 3/2 * x + 6

y = 2/3 * x - 1

y = 1/2 * x - 1

y = 4x - 2

Answer 1

To determine which equation among the options could have a solution of (6, 2), we need to substitute \( x = 6 \) into each equation and check if we get \( y = 2 \).

1. **For** \( y = -\frac{3}{2}x + 6 \):
\[
y = -\frac{3}{2}(6) + 6 = -9 + 6 = -3 \quad \text{(not (6, 2))}
\]

2. **For** \( y = \frac{2}{3}x - 1 \):
\[
y = \frac{2}{3}(6) - 1 = 4 - 1 = 3 \quad \text{(not (6, 2))}
\]

3. **For** \( y = \frac{1}{2}x - 1 \):
\[
y = \frac{1}{2}(6) - 1 = 3 - 1 = 2 \quad \text{(this is (6, 2))}
\]

4. **For** \( y = 4x - 2 \):
\[
y = 4(6) - 2 = 24 - 2 = 22 \quad \text{(not (6, 2))}
\]

Among the equations provided, the equation \( y = \frac{1}{2}x - 1 \) gives the solution (6, 2).