For which value of c will the equation 3x + c = 3x + 2 have no solution? Select all that apply.A. 2B. 3C. 4 D. 5

Accepted Solution

Answer:B. 3C. 4D. 5Step-by-step explanation:Given equation:[tex]3x+c=3x+2[/tex]For a system of linear equations to have no solution the equations of line must be parallel to each other but not lie on same lines i.e. the slopes of the lines must be same but the y-intercepts must be different.∴ For an equation to have no solutions the equation must be in the form:[tex]mx+k=mx+l[/tex] where [tex]k\neq l[/tex] where [tex]m[/tex] represents slope of equations and [tex]k,l[/tex] are the y-intercepts of the line.For the given equation to have no solution [tex]c[/tex] must be a number which is [tex]\neq 2[/tex] because if [tex]c=2[/tex] then the left side will be =to right side of the equation making it infinite solutions. Thus, from the given choices the values of [tex]c[/tex] which makes the equation with no solutions are:3,4,5