Identify the solution(s) of the system of equations, if any.
3x-2y=6
5x=5-25y
A) (28/13, 3/13)
B) (-3/17, 32/17)
C) (32/17, -3/17)
D) (32/9, 7/3)
I think the answer is D but i did my check and still comes out incorrect
It's C.
You solve the bottom equation for x, then you plug that into where the x is on the top equation.
3(1-5y)-2y=6
Solve for y, and then for x
change 2nd equation by dividing by 5
x = 1 - 5y
sub into the 1st
3(1-5y) - 2y = 6
3 - 15y - 2y = 6
-17y = 3
y = -3/17
Without even going further, the only one that has that y value is C)
I will leave it up to you to check that the x is correct by subbing my answer back into x = 1 - 5y
All you do to check x is to take the y answer and plug it into the top equation and solve for x
Thank you Kimmy!!
You are welcome!
To find the solution(s) to the system of equations, we need to solve the equations simultaneously and check if the obtained values for x and y satisfy both equations.
Let's start by solving the system of equations:
Equation 1: 3x - 2y = 6
Equation 2: 5x = 5 - 25y
First, let's rearrange Equation 1 to isolate x:
3x = 2y + 6
x = (2y + 6) / 3
Now, substitute this expression for x in Equation 2:
5((2y + 6) / 3) = 5 - 25y
Multiply both sides of the equation by 3 to eliminate the fraction:
10y + 30 = 15 - 75y
Combine like terms:
85y = -15
Divide by 85:
y = -15/85
Simplify:
y = -3/17
Now that we have the value for y, we can substitute it back into Equation 1 to find the corresponding x:
3x - 2(-3/17) = 6
Multiply both sides by 17 to eliminate the fraction:
51x + 6 = 102
Subtract 6 from both sides:
51x = 96
Divide by 51:
x = 96/51
Simplify:
x = 32/17
Therefore, the solution to the system of equations is (32/17, -3/17).
So, the correct answer is:
C) (32/17, -3/17)
If you have checked your answer and it still comes out incorrect, it's possible that there was an error in your calculations. Please double-check your work to ensure accuracy.