Question

Given the system of linear equations:

{
y=−5
y=3x−2
​


Part A: Graph the system of linear equations.

Part B: Use the graph created in Part A to determine the solution to the system.

Part C: Algebraically verify the solution from Part B.

Answer 1

Part A — Graph instructions
- Line 1: y = −5 is a horizontal line through (0, −5). Plot e.g. (−2, −5), (0, −5), (2, −5).
- Line 2: y = 3x − 2 has slope 3 and y-intercept −2. Plot e.g. (0, −2), (1, 1), (−1, −5).

The two lines intersect at the point where they meet (shown by the common point (−1, −5)).

Part B — Solution from the graph
- The intersection point (solution) is (x, y) = (−1, −5).

Part C — Algebraic verification
- Set the two expressions for y equal: −5 = 3x − 2.
- Solve: 3x = −3 ⇒ x = −1.
- Then y = −5 (given) and y from the second equation: y = 3(−1) − 2 = −3 − 2 = −5.
- Both equations give (−1, −5), so the solution (−1, −5) is verified.