Question

Q1)How many solutions does the pair of equations y = 0 and y = -5 have?

Answer 1

Linear Equations

→ An equation that pairs of solutions draws a line on the plane.

Graphical Method

→ An intersection of two graphs is a common solution.

Solution

(The 1st Attachment)

y=0 and y=-5 represent a pair of lines on the plane.

However, two lines are parallel. There is no point of intersection. So, no common solutions exist.

There is no solution for the pair of equations.

More information

(The 2nd Attachment)

A fact about line

y=ax+b represents a line on a plane.

To show is simple. Raise x-axis to y=b. Now, the line represents y=ax , which is proportional.

We can make infinitely many similar triangles with y=ax , so the line is a hypotenuse of a triangle, which is a line.

This also proves why the slope is constant in a line.

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