Question

Graph and check to solve the linear system. $$ \begin{aligned} y &=-6 \\ x &=6 \end{aligned} $$

Short answer

The solution to the system of equations is the point (6,-6).

Step-by-step solution

Graph the equation \(y = -6\)

Start by graphing the line \(y = -6\) which is a horizontal line across the y-axis at the point -6. This line has a slope of 0 and runs parallel to the x-axis.

Graph the equation \(x = 6\)

Next, graph the line \(x = 6\) which is a vertical line on x-axis at the point 6. This line runs parallel to the y-axis.

Find the intersection point

Now, determine the point where both of these lines intersect. This intersection point is the solution to the system of equations.

Verify the solution

Finally, verify the solution by substituting \(x = 6\) and \(y = -6\) into both equations. If both equations are satisfied, then the solution is correct.