Question

Two lines form a linear system. The slope of one line is 4 and it has a y-intercept of (0, -3). The slope of the other line is 4 and it has a y-intercept of (0, 8). How many solutions does this system have?

Answer 1

The system of equations with parallel lines having the same slope but different y-intercepts has no solutions.

Step-by-step explanation:

When we look at a linear system of equations, the number of solutions is determined by the slopes and y-intercepts of the lines. In this case, both lines have the same slope of 4, but different y-intercepts, one being (0, -3) and the other (0, 8). This means we are looking at parallel lines, which never intersect.

Parallel lines have the same slope but different y-intercepts. Because they will never meet, this system of equations has no solutions. It is also important to remember that in slope-intercept form, the equation of a line is written as y = mx + b, where m is the slope and b is the y-intercept.