Question

Solve the system of equations y = –2x + 8 and y = x – 4. What is the solution?

a) (0, 4)
b) (4, 0)
c) (–12, 32)
d) (–1.33, –5.33)

Answer 1

Option b) (4, 0) is the correct answer. To solve the system of equations y = -2x + 8 and y = x - 4, we can set the two equations equal to each other and solve for the value of x. After finding the value of x, we can substitute it into either equation to find the value of y. The solution is (4, 0).

Step-by-step explanation:

To solve the system of equations y = -2x + 8 and y = x - 4, we can set the two equations equal to each other:
-2x + 8 = x - 4
Next, we can simplify and solve for x:
-2x - x = -4 - 8
-3x = -12
x = -12 / -3
x = 4

Now that we have the value of x, we can substitute it into either equation to find the value of y:
y = -2(4) + 8
y = -8 + 8
y = 0

Therefore, the solution to the system of equations is (4, 0). Option b) (4, 0) is the correct answer.