Which of the following ordered pairs represents the solution to the system of equations below?
-3x+2y=2
7x-3y=7
[8.EE.8.b]
A. (2, 4)
B. (4, 7)
C. (7, 14)
D. (8, 13)
Use trial and error. Which pair fits the problems?
To find the solution to the system of equations, we need to solve the equations simultaneously by using either substitution or elimination method. Let's use the elimination method.
-3x + 2y = 2 (Equation 1)
7x - 3y = 7 (Equation 2)
To eliminate one of the variables, we can multiply Equation 1 by 7 and Equation 2 by 3:
-21x + 14y = 14 (Equation 3)
21x - 9y = 21 (Equation 4)
Now, add Equation 3 and Equation 4:
(-21x + 14y) + (21x - 9y) = 14 + 21
-21x + 21x + 14y - 9y = 35
5y = 35
y = 35/5
y = 7
Substitute the value of y into Equation 1:
-3x + 2(7) = 2
-3x + 14 = 2
-3x = 2 - 14
-3x = -12
x = -12/-3
x = 4
So, the solution to the system of equations is (4, 7).
Therefore, the answer is option B. (4, 7).
To find the solution to the given system of equations, we can solve it using the method of substitution or the method of elimination. Let's use the method of substitution.
The given system of equations is:
-3x + 2y = 2 ...(1)
7x - 3y = 7 ...(2)
We can solve equation (1) for x:
-3x = 2 - 2y
x = (2 - 2y)/(-3)
Now substitute the value of x in equation (2):
7((2 - 2y)/(-3)) - 3y = 7
Multiply through by -3 to clear the fraction:
-21 + 14y - 3y = -21
Combine like terms:
11y = 0
Divide by 11:
y = 0
Now substitute this value of y back into equation (1):
-3x + 2(0) = 2
-3x = 2
x = 2/(-3)
x = -2/3
So, the solution to the system of equations is the ordered pair (-2/3, 0).
Now let's check which of the given options represents this solution:
A. (2, 4) - Incorrect
B. (4, 7) - Incorrect
C. (7, 14) - Incorrect
D. (-2/3, 0) - Correct
Therefore, the correct answer is option D: (8, 13).