Is this system of equations consistent, inconsistent, or dependent?

Question

4x - 3y = 15

7y - 35 = 9 (1/3) x

*9 (1/3) is a mixed number (9 and one-third)*

Answer 1

Jesset, now that you’ve explained that 9(1/3)x means (9+1/3)x, it’s a new problem. Please show your work so far so that we can advise you. Since nearly all of your answers are correct, I’m confident that you know how to do this.

Answer 2

First of all the understanding of each possible answer for this question comes from: If a system of equations has exactly one solution, it is independent or consistent. If a system of equations has an infinite number of solutions, it is dependent, where you graph the equations and both equations represent the same line. If a system of equations has no solution, it is said to be inconsistent.

Second, assuming your description of 9(1/3)x is equal to 3x, your answer is consistent and here is how:

Step 1: Rearrange the second equation to : -3x + 7y = 35.

Step 2: Solving the system of equations for our y-value, by multiplying the top by 3 and bottom by 4:

(4x - 3y = 15) * (3) => 12x - 9y = 45 => adding the equations together => 19y = 185

(-3x + 7y = 35) * (4) => -12x + 28y = 140 => , so our distinct y-value is : y = (185/19)

Step 3: Performing step 2, but for our x-value, but this time multiplying the top by 7 and bottom by 3:

(4x - 3y = 15) * (7) => 28x - 21y = 105 => adding the equations together => 19x = 210

(-3x + 7y = 35) * (3) => -9x + 21y = 105 => , so our distinct y-value is : x = (210/19)

Because this system has exactly one solution it is consistent.