Question

What is the correct classification of the system of equations below?

5x + 6y = 1
y = -5x + 6

A) parallel
B) coincident
C) intersecting

Answer 1

The correct classification is: c) intersecting

Answer 2

Intersecting

Explanation:

5x + 6y = 1

y = -5x + 6

Solve the first equation for y

5x +6y =1

Subtract 5x on both sides

6y= -5x +1

Now divide each term by 6

`y= (-5x)/(6) + (1)/(6)` , slope = -5/6

y= -5x + 6 is the second equation, slope = -5

We got equation in the form of y = mx + b

When the slopes (m) are equal then the lines are parallel

When the slopes(m) and y intercept b are equal then the lines are coincident

In both the equations the slopes are not same, So they are intersecting lines.

Both lines intersects at a point.