Question

1. An equation is shown below.

2x + y = 3

Part A: Explain how you will show all of the solutions that satisfy this equation. (4 points)

Part B: Determine three different solutions for this equation. (4 points)

Part C: Write an equation that can be paired with the given equation in order to form a system of equations that is inconsistent.

Answer 1

A) We can first start with the how: our equation is 2x+y=3. First, subtract 2x from each side. We get y=-2x+3. Our Y variable is isolated.
B) Now we can describe which points our equation goes through. One of them is obvious in our form, and that is (0,3) or our y-intercept. Another 2 would be branching off that line, such as (1,1) or (-1,5)
C) To make our system inconsistent, we can easily make another equation, with same slope, but the y-intercept has to be different. Our equation can be y=-2x+2, y=-2x+4, or even y=-2x+3.00000001.

Hope this helps you.