PLEASE HELP!!!!! I would like to have this explained.

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4–x and y = 2x + 3 intersect are the solutions of the equation 4–x = 2x + 3. (4 points)

Part B: Make tables to find the solution to 4–x = 2x + 3. Take the integer values of x between −3 and 3. (4 points)

Part C: How can you solve the equation 4–x = 2x + 3 graphically? (2 points)

Question

PLEASE HELP!!!!! I would like to have this explained.

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4–x and y = 2x + 3 intersect are the solutions of the equation 4–x = 2x + 3. (4 points)

Part B: Make tables to find the solution to 4–x = 2x + 3. Take the integer values of x between −3 and 3. (4 points)

Part C: How can you solve the equation 4–x = 2x + 3 graphically? (2 points)

anonymous · Answer

I just need A

anonymous · Answer

PART A

It's how we basically solve the "where exactly do these two lines intersect" type of problem. 

Baiscally, the two equations (y=4-x and y=2x+3) describe the graph of a straight line (hence why they are called "linear equations"). Two lines in Euclidian space which are not parallel are going to intersect/cross each other at some point. 

If you recall, the way we graph equations is by basically assigning two arbitrary values for x and then plugging them into the equation to get the corresponding values for y. The reason we only need two such pairs is because (since we already know the graph is going to be a line) we only need a minimum two points to draw a straight line. 

Now, let's think about what happens when two lines intersect. If the lines are straight and non parallel to each other then there will be exactly 1 point at which they will cross each other, right? 

Reflect upon this point for a second: the point of intersection has the "unique" property of being a solution for both lines which cross it since it belongs on both of their respective graphs.

anonymous · Answer

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anonymous · Answer

I have already made a graph and they intercept at -0.5, 2.

anonymous · Answer

Yes - but it's asking you why, isn't it ?

anonymous · Answer

Can you just give me an answer, please? It's a question that messes with my head.

anonymous · Answer

I just did. Which part of my answer don't you understand though ?

anonymous · Answer

You're graphing two lines, those two lines intersect at a point. That point has to satisfy both equations for both lines because it's at the intersection of those two lines. That's why the x coordinates are the solution for that equation.