Question

How do i do this
Without graphing, is the system independent, dependent, or inconsistent?

Answer 1

Since the second equation is already solved for y, use the substitution method and plug in y of the second equation into the first equation. Then solve for x. What do you get?

Answer 2

I think so... One sec let me try it

Answer 3

15

Answer 4

12x + 3y = 12
y = -4x + 5

Plug in -4x + 5 into y of the first equation.

12x + 3(-4x + 5) = 12

Now simplify the left side.

Answer 5

12x + -12x + 15

Answer 6

Good, but keep the right side there also.
You have
12x - 12x + 15 = 12
The left side can be simplified by combining the two x-terms together. Do that. What do you get?

Answer 7

15 =/= 12?

Answer 8

12x - 12x = 0 + 15 = 12
15 doesn't equal 12 tho

Answer 9

You actually get 15 = 12, which you know is false. That means the system of equations has no solution. It is inconsistent.

Answer 10

ok what about if it was dependent?

Answer 11

When you are dealing with systems of 2 linear equations, you have these possibilities:
1. An independent system has 1 solution. It is represented graphically by two intersecting lines. Two lines can only intersect in 1 point.
2. A dependent system has an infinite number of solutions. The two equations are really the same equation. Think of it as a line on top of itself. Any point on the line is a solution. That's why there is an infinite number of solutions.
3. An inconsistent system has no solution. Graphically, it is represented by two parallel lines. Parallel lines do not intersect. All the points on one line are solutions to the equation of that line but not the other, and vice versa. There is no point that is on both lines.

Answer 12

I hope the above explains it.