Find the solution for y=1/2 x + 2 and y=-1/4x+8

Answer 1

To find the solution for the system of equations y = (1/2)x + 2 and y = (-1/4)x + 8, we can set the two equations equal to each other:

(1/2)x + 2 = (-1/4)x + 8

Next, we can get rid of the fractions by multiplying both sides of the equation by 4:

4 * ((1/2)x + 2) = 4 * ((-1/4)x + 8)
2x + 8 = -x + 32

Now, we can isolate the x-term by adding x to both sides:

2x + x + 8 = -x + x + 32
3x + 8 = 32

Next, we can isolate the constant term by subtracting 8 from both sides:

3x + 8 - 8 = 32 - 8
3x = 24

Now, we can solve for x by dividing both sides by 3:

(3x)/3 = 24/3
x = 8

Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation y = (1/2)x + 2:

y = (1/2)(8) + 2
y = 4 + 2
y = 6

Therefore, the solution to the system of equations y = (1/2)x + 2 and y = (-1/4)x + 8 is x = 8 and y = 6.