Respuesta :
let's recall that perpendicular lines have negative reciprocal slopes, so say for a line with a slope of a/b
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{a}{b}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{b}{a}}\qquad \stackrel{negative~reciprocal}{-\cfrac{b}{a}}}[/tex]
a perpendicular one will be -b/a.
what does that mean? well, that the lines are perpendicular of course, they meet at a 90° angle, and two straight lines meeting at 90° can only meet once.
since a solution to a system of equations is where the graph meet, and these two meet perpendicularly once, then that means only one solution.
The system of equation will have one solution.
The correct answer is an option (B)
What is a system of equation ?
It is a collection of one or more linear equation involving the same variable.
For given question,
Two equations have negative reciprocal slope .
Which means if one equation have slope = m
then slope of other equation will be = -1/m
This means, both the lines are perpendicular to each other , hence both the lines must be intersecting each other at one point.
In system of equation , the solution of the two equation is the point where they intersect .
Since, both the lines are intersecting at one point . Hence, it will have only one solution.
Therefore, the correct answer is an option b) the system will have one solution
Learn more about the system of equations here:
https://brainly.com/question/12895249
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