Question

Which graph represents the solution to the given system? y = -4x +4 y = 1/2 x -2

Answer 1

Graph 1 is the correct answer.

Answer 2

Answer:
first one

Explanation:
The solution of the system of equation is the point that satisfies both equations.
In other words, it is the point of intersection between the two lines.

Now, we will use algebra to get the solution as follows:
The first given equation is:
y = -4x + 4 .........> equation I

The second given equation is:
y = 1/2 x - 2 ..........> equation II

Substitute with equation I in equation II and solve for x as follows:
y = 1/2 x - 2
-4x + 4 = 0.5x - 2
4 + 2 = 0.5x + 4x
6 = 4.5 x
x = 4/3

Now, substitute with x in equation I to get y as follows:
y = -4x + 4
y = -4(4/3) + 4
y = -4/3

Based on the above, the solution of the system is (4/3 , -4/3)

Therefore, the correct graph will be the one having the point of intersection (4/3 , -4/3) which is the first one.

I have also attached the graph below.

Hope this helps :)