Solving Linear Equations: Inconsistent, Dependent & Independent

[torid]

solve each system of linear equations. Indicate whether each system is inconsistant, dependent, or independent.

i'm not sure how to get these problems into slope intercept form: y=mx+b

1.
3x - 6y=9
1/2x=y +3/2

2.
2x + 3y=1
-3x + 4y=-10

3.
0.5x - 0.75y=0.125
4x-6y=12

if anyone could explain to me how to do these problems, that would be great.
i just don't understand how to get them into slope.
but i do get how to graph them.

 

[Dick]

You don't get them into slope-intercept form. You just solve them or show you can't. Solve one equation, for example, for x and substitute that expression into the other equation.

 

[torid]

yeah. but i do need them in slope intercept form, so maybe you could explain how i get them there.

 

[Dick]

yeah. but i do need them in slope intercept form, so maybe you could explain how i get them there.

No, you don't get need them in slope intercept form. I'll give you a big hint, the solution to the first one is x=6, y=3/2. That's a single point. You don't express that in slope intercept form. It's a POINT. Now, how did I get that solution?

 

[HallsofIvy]

Please explain why you need to get them in slope intercept form? If the problem requires you to do that, why didn't you say so in your first post? You said the problem was to "Indicate whether each system is inconsistant, dependent, or independent"! That has little to do with "slope intercept" form. And, I should point out that "problem" don't have a slope intercept form so it is unclear what you mean by "get these problems into slope intercept form"!

If you mean get each equation into slope intercept form (again, not necessary for doing what you first said you wanted to do nor even a good idea), you say, correctly, that slope intercept form is "y= mx+ b". Do you notice the "y" alone on the left side? Solve each equation for y. If you know what slope intercept form is, or are working on systems of equations, you certainly should know how to solve a single linear equation.