Without plotting the functions, find the points of the graph y = -7x + 8, where the abscissa

Without plotting the functions, find the points of the graph y = -7x + 8, where the abscissa and ordinate are opposite numbers.

We need to find the points of the graph y = -7x + 8, where the abscissa and ordinate are opposite numbers, without performing the graphing of functions. To do this, we will compose and solve a linear equation.

So, the abscissa and ordinate must be opposite numbers:

y = -x.

We substitute functions instead of y = -x in the equations and solve the resulting linear equation in one variable.

-x = -7x + 8;

We group the terms with and without variables in different parts of the equation.

-x + 7x = 8;

6x = 8;

We are looking for an unknown factor:

x = 8: 6;

x = 1 1/3.

The point has coordinates (1 1/3; -1 1/3).