Question

Solve the system of equations by graphing y=-x and y=x-6.

Answer 1

To solve the system of equations y = -x and y = x - 6 by graphing, one must graph both lines and find their intersection point. The lines intersect at the point (3, -3), making the solution to the system x = 3, y = -3.

Step-by-step explanation:

To solve the system of equations by graphing y = -x and y = x - 6, we plot both equations on the same coordinate system.

Steps to Graph the Equations

1. Graph the equation y = -x. This is a straight line with a slope of -1, which means it goes down 1 unit on the y-axis for every increase of 1 unit on the x-axis. It passes through the origin since its y-intercept is 0.
2. Graph the equation y = x - 6. This line has a slope of 1, meaning it rises 1 unit on the y-axis for every increase of 1 unit on the x-axis. Its y-intercept is -6, as the line crosses the y-axis at (0, -6).
3. Identify the point where both lines intersect. This point of intersection is the solution to the system of equations.

By graphing these lines, it's evident that both lines are perpendicular and intersect at the point (3, -3). Therefore, the solution to the system of equations is x = 3, y = -3.