Question

a system of equations has no solution. if y = 8x 7 is one of the equations, which could be the other equation? y = 8x 7 y = 8x – 7 y = –8x 7 y = –8x – 7

Answer 1

A system of equations has no solution when the lines representing the equation are parallel but do not coincide. For two lines to be parallel, the must have the same gradient i.e. coeficient of x when y is made the subject of formular must be equal.
If one of the equations is y = 8x + 7, then the other equation will be y = 8x - 7

Answer 2

The given equation in two variable is

$y= 8 x \pm7$

The two equation in two variables are

Ax + By +C=0

P x + Q y +R=0  

the condition that  these two equation has no solution if,

$\frac{A}{P}= \frac{B}{Q}\neq \frac{C}{R}$

Or in terms of line , if the two lines have same slope.

For example, y= a x + b and , y= a x+p are two lines having same slope means they are parallel, that is they will never intersect.

If the line is , y= 8 x + 7, the other line will be, among the given options, y= 8 x -7, will be other line.→Option (B)

If , y= 8 x -7 is one line, the other line will be , y= 8 x + 7.