Use the graph to answer the question, y = x - 6 and y = -x + 4
Review the graphs of a system of two linear equations in two variables: y = x - 6 and y = -x + 4. Find the solution to both equations.
To find the solution to both equations, we need to find the point where the two lines intersect on the graph.
The graph of y = x - 6 is a line passing through the point (0, -6) and (6, 0).
The graph of y = -x + 4 is a line passing through the point (0, 4) and (4, 0).
To find the intersection point of these two lines, we set the two equations equal to each other:
x - 6 = -x + 4
2x = 10
x = 5
Now that we have found x = 5, we can substitute this back into either of the original equations to find y:
y = x - 6
y = 5 - 6
y = -1
Therefore, the solution to the system of equations is x = 5 and y = -1. This is the point at which the two lines intersect on the graph.