Final answer:
Rewriting Equation A to have a y-intercept of −4 changes its form to y = −3x −4. Though both equations then share the y-intercept, they still have different slopes and will intersect at a new point, altering the solution to the system.
Step-by-step explanation:
If equation A (y = −3x) were rewritten so that the y-intercept became −4, the new equation would become y = −3x −4. Comparing this with Equation B (y = −x −4), it is clear that both equations now have the same y-intercept but different slopes. The original system of equations consisted of two lines with different slopes and different y-intercepts, which would intersect at a single point, providing a unique solution to the system.
However, with the change in the y-intercept of Equation A, the two equations still have different slopes, which means the lines are not parallel and will intersect.
But now, since both equations have the same y-intercept, the point of intersection will move along the line y = −x −4 to a new position. The lines will intersect at the point where their x-values are equal (since the y-values are already the same due to equal y-intercepts). In other words, the solution to the system will change, but the system will still have a single solution where the two lines intersect.