Which graph represents a solution given system y = -x + 2y = -1/2 x + 8
To find the graph that represents the solution to the given system, we first need to solve the system of equations.
The given system is:
y = -x + 2 ...(1)
y = -1/2x + 8 ...(2)
To solve this system, we can substitute equation (1) into equation (2) for y:
-x + 2 = -1/2x + 8
Next, let's solve for x:
Multiply everything by 2 to eliminate the fraction:
-2x + 4 = -x + 16
Add x to both sides:
-x -2x + 4 = -x - x + 16
-3x + 4 = 16
Subtract 4 from both sides:
-3x + 4 - 4 = 16 - 4
-3x = 12
Divide by -3:
x = -4
Now, substitute this value of x back into equation (1) or (2):
y = -(-4) + 2
y = 4 + 2
y = 6
So, the solution to the system is x = -4 and y = 6.
Now, let's look at the graphs:
Graph 1:
-4 ──► ──► ──► ──► ───► ───►
1 2 3 4 5
Graph 2:
6 ──► ──► ──► ──► ───► ───►
1 2 3 4 5
From the graphs, it can be seen that the point (-4, 6) satisfies both equations. Therefore, the graph that represents the solution to the given system is Graph 2, with the point (-4, 6) plotted on it.