Question

Consider this system of linear equations: y = –3x + 5 y = mx + b Which values of m and b will create a system of linear equations with no solution? m = –3 and b = –3 m = 5 and b = –3 m = 3 and b = 5 m = -3 and b = 5

Answer 1

To create a system of linear equations with no solution, the slopes of the lines must be equal, but the y-intercepts must be different. In this case, m = -3 and b = 5 will create a system of linear equations with no solution.

Step-by-step explanation:

To create a system of linear equations with no solution, the lines represented by the equations must be parallel. This means that the slopes of the lines must be equal, but the y-intercepts must be different.

In the given system of linear equations, the equation y = –3x + 5 has a slope of -3 and a y-intercept of 5. So, to create a system of linear equations with no solution, we need to choose the values of m and b in the equation y = mx + b such that the slope, m, is -3 and the y-intercept, b, is not equal to 5.

Therefore, m = -3 and b = 5 will create a system of linear equations with no solution.