80 points math question! explain in simple terms : )

make a graph also. the main reason i'm asking this question for such high points is for you to explain your answer and how you got it. i really want to understand.

An absolute value function has a graph that is V shaped.

The domain is the input (x) value, which can be any real number, so the domain is (-∞,∞)

The range starts at the vertex and goes to infinity.

To find the vertex, set the absolute value part of the equation to 0 and solve for x:

x+3 = 0. x = -3

Now replace x with -3 and solve the full equation:

|-3 +3|-1 = -1

The vertex becomes (-3,-1)

The range is the output value ( Y) , so the range would be [-1,∞)

See attached picture for graph:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

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step-by-step explanation: