Question

4 draw a line in each coordinate plane so that the lines represent a system of equations with the given number of solutions.
a. no solution
b. exactly one solution
c. infinitely many solutions

Explanation:

Step1: Identify target line property

For exactly one solution, the second line must intersect the given line (which is $y=-x$) at exactly one point, so it must have a different slope.

Step2: Choose a line with new slope

Select a line with a non-$-1$ slope, e.g., $y=x$. This line passes through $(0,0)$ and $(1,1)$, intersecting $y=-x$ only at the origin.

Step3: Plot the new line

On the coordinate plane, mark points $(0,0)$ and $(1,1)$, then draw a straight line through them.

Answer:

Draw a line with a slope different from the given line (e.g., the line $y=x$, passing through points like $(0,0)$ and $(1,1)$) on the coordinate plane for part b. This creates a system with exactly one solution (the intersection point $(0,0)$).