PLEASE SEND HELP THIS IS A TIMED TEST!! SYSTEMS OF EQUATIONS.

can i know which language is this?

option a is correct.

only one solution to the system of equations

step-by-step explanation:

if the graph of the equations do not intersects(i.,e if they are parallel) then, there are no solutions that are true for both the equations.

if the graph of the equations intersects, then there is one solution and that is true for both the equations.

since, in the given figure:

the two lines intersect each other

⇒there is only one solution which satisfy both the lines of an equations.

therefore, there is only one solution to the system of equation

we have been given a piecewise function which has three parts

we can graph each part one by one.

first part is x+1 which is just like equation y=x+1

restriction with first part is x< 0 so that means we can use any number for x which is less than 0 for example x=-1 and x=-2

now plug x=-1 into y=x+1 to get y

y=x+1=-1+1=0

so the point will be (-1,0)

similarly we get another point (-2,-1)

now we graph a line joining both points but keep in mind that line must be on left side of x=0 because of restriction x< 0

same way we can graph 2nd and third parts

if we have < or > then we use open circle.

if we have < = or > = then we use close circle.

so using above information, final graph can be drawn as: