To solve the system of equations by graphing, you can start by rearranging each equation to solve for y in terms of x:
64x + 8y = 8
8y = -64x + 8
y = -8x + 1
8x + y = 1
y = -8x + 1
Now, both equations are in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
The two equations are the same, which means they represent the same line on the graph. In this case, the system of equations is dependent, and there are infinitely many solutions, as the two equations describe the same line.
When you graph the line y = -8x + 1, you will see a single line on the coordinate plane.
To check the answer algebraically, you can see that the two equations are equivalent, and when you substitute one equation into the other, they are both satisfied:
64x + 8y = 8
64x + 8(-8x + 1) = 8
64x - 64x + 8 = 8
8 = 8
Since the left side of the equation equals the right side, this confirms that the two equations are equivalent and that there are infinitely many solutions.