Analyze the solution set of the following system by

following the given steps.

2x + y = 5

3y = 9 - 6x

Write each equation in slope-intercept form.

y =

x +

x +

Y

=

Why do the equations have in common?

see explanation

Step-by-step explanation:

The equation of a line in slope - intercept form is

y = mx + c (m is the slope and c the y - intercept)

Rearrange the given equations into this form

2x + y = 5 (subtract 2x from both sides)

y = - 2x + 5 ← in slope - intercept form

3y = 9 - 6x (divide all terms by 3)

y = 3 - 2x = - 2x + 3 ← in slope - intercept form

We have

y = - 2x + 5 and y = - 2x + 3

Both equations have a slope m = - 2

The equations of lines with equal slopes are Parallel lines

They all Intercept form