Question

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 +
y =
be+
DONE
What do the equations have in common and how are they different

Answer 1

Slope -intercept for of equation 1:
`y=-2x+5`

Slope -intercept for of equation 2:
`y=-2x+3`

Looking at slope-intercept form of both equations, we have slope m = -2

Both have same slopes so, the lines are parallel.

Explanation:

We need to write equations in slope-intercept form.

The general formula of slope-intercept form is:
`y=mx+b` where m is slope and b is y-intercept.

The first equation is:

`2x+y=5`

Slope-intercept form:

`y=-2x+5`

The second equation is:
`3y=9-6x`

Rearranging:
`3y=-6x+9`

Slope-intercept form:

`y=(-6)/(3) x +(9)/(3)\\y=-2x+3`

Slope -intercept for of equation 1:
`y=-2x+5`

Slope -intercept for of equation 2:
`y=-2x+3`

Looking at slope-intercept form of both equations, we have slope m = -2

Both have same slopes so, the lines are parallel.

They have different y-intercepts.