Without graph, the system is independent, dependent or inconsistent y=2x-8 2x-y=8
An independent system has different slopes, so it has a unique solution. If two lines have the same slope, then they are inconsistent. The reason is that both rows can have NO SOLUTION or INFINITELY SOLUTIONS. An incoherent system that has infinitely many solutions is said to be dependent. Now let’s do the thing in both equations, to get, For the second equation, we have Wow, both systems have the same slope and intercept. This means that the system has infinite solutions, so it is dependent. Both systems depend
can be dependent
1. independent 2. inconsistent
2x – y = 8 |-2x -y = -2x + 8 |·(-1) y = 2x – 8 The two equations are equal, so the system is dependent.
Answer 6
I would say it’s independent
Answer 7
Independent walkthrough: We need to determine if the system of equations and are independent, dependent, or inconsistent. Now, we know that the general form of a linear equation in two variables is So, the general form of the given equations is and Now, for a system of equations and , we need to find , and Now, Then, we have So , the system of equations is independent.
Putting the equations into a standard form helps me identify dependent and inconsistent systems. In standard form, the leading coefficient is positive and all numbers are coprime to each other (have no common factors). 1.) 2x + y = -9. . . . . . multiply the original equation by -1 … 3x – 4y = -8 . . . . . . the system is independent These two equations will give rise to a single solution. 2.) 4x + y = 4 . . . . . . divide the original equation by 3…4x + y = 5. . . . . . . the system is inconsistent These two equations describe parallel lines, so they will not have a point of intersection. There are no values of x and y that satisfy both equations.
The answers you seek my friend 1. D 2.A 3.B 4.C (independent) 5. B
0
Without graphs, the system -2x – y = 9 and 3x – 4y = -8 is independent and consistent. Solution: Given, the system of equations is -2x – y = 9 and 3x – 4y = -8
We need to find the type of equations, i.e. independent or dependent or inconsistent.
Now for this we have to solve the given system of equations to get a conclusion.
So now -2x – y = 9 ⇒ 2x + y = -9 ⇒ (1) and 3x – 4y = -8 → (2)
Here we need to multiply (1) by 4 to cancel one of the terms.
So, by solving (1) and (2)
11x + 0 = -44
x = -4
Substitute the x value in (1)
2(-4) + y = -9
-8 + y = -9
y = 8 – 9
y = -1
Therefore, the system of equations is consistent and independent because two equations represent different equations.
Therefore, the systems of equations are independent and consistent.