Classify this system of equations:
5x + y = 19
x + 5y = 23
a) consistent, independent
b) inconsistent
c) inconsistent, dependent
d) dependent
Would elimination or substitution be the way to solve this? I tried both ways and I either got a negative or a strange decimal. Thanks!
Just inspecting it, the lines are perpendicular, so they are definitiely consistent. Now if you don't know how to recognize that, you can solve it by elimination. multipy the first equation by 5
25x+5y=95 then subtract the second equation
24x=95-23 solve for x, then go back and use either of the equations to find y. It looks in decimal not simple, I would leave it in fractions (x=74/24=37/12 I think, check it)
To classify a system of equations, we need to determine whether it is consistent or inconsistent, and whether it is independent or dependent.
To solve this system of equations, we can use either the method of elimination or substitution.
Let's use the method of elimination to solve this system:
5x + y = 19
x + 5y = 23
To eliminate one of the variables, let's multiply the first equation by (-1) and the second equation by 5:
-5x - y = -19
5x + 25y = 115
Now, adding the two equations together, we can eliminate x:
(-5x -y) + (5x + 25y) = (-19) + (115)
24y = 96
Dividing both sides by 24, we get:
y = 4
Substituting y = 4 back into one of the original equations, let's use the first equation:
5x + 4 = 19
Solving for x, we have:
5x = 19 - 4
5x = 15
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 4.
Now, let's classify the system:
Since we obtained a unique solution (x = 3 and y = 4) and the solution satisfies both equations, the system is consistent.
Next, to check whether the system is independent or dependent, we need to determine if the two equations are multiples of each other or not. In this case, the two equations are not multiples of each other, so the system is independent.
Therefore, the classification of this system of equations is: a) consistent, independent.