Question
                Solve the systems of equations.
5x + 2y = 14
x - 6y = 22
(___, ___)
            
        5x + 2y = 14
x - 6y = 22
(___, ___)
Answers
                    Answer
            
    wrong answer
    
                    Answered by
            GPT 3.5
            
    To solve this system of equations, we can use the method of substitution or linear combination. Let's use the substitution method.
From the first equation:
5x + 2y = 14
y = (14 - 5x) / 2
Substitute this value of y into the second equation:
x - 6((14 - 5x) / 2) = 22
x - 42 + 15x = 44
16x - 42 = 44
16x = 86
x = 86 / 16
x = 5.375
Now substitute the value of x back into the first equation to find y:
5(5.375) + 2y = 14
26.875 + 2y = 14
2y = 14 - 26.875
2y = -12.875
y = -12.875 / 2
y = -6.4375
Therefore, the solution to the system of equations is (5.375, -6.4375).
    
From the first equation:
5x + 2y = 14
y = (14 - 5x) / 2
Substitute this value of y into the second equation:
x - 6((14 - 5x) / 2) = 22
x - 42 + 15x = 44
16x - 42 = 44
16x = 86
x = 86 / 16
x = 5.375
Now substitute the value of x back into the first equation to find y:
5(5.375) + 2y = 14
26.875 + 2y = 14
2y = 14 - 26.875
2y = -12.875
y = -12.875 / 2
y = -6.4375
Therefore, the solution to the system of equations is (5.375, -6.4375).
                    Answered by
            GPT 3.5
            
    My apologies. Let me try again:
Using the substitution method to solve the system of equations:
5x + 2y = 14 (1)
x - 6y = 22 (2)
From equation (2), we can express x in terms of y:
x = 22 + 6y (3)
Now, substitute the expression for x from equation (3) into equation (1):
5(22 + 6y) + 2y = 14
110 + 30y + 2y = 14
32y = -96
y = -96 / 32
y = -3
Now, substitute the value of y back into equation (3) to find x:
x = 22 + 6(-3)
x = 22 - 18
x = 4
Therefore, the correct solution to the system of equations is (4, -3).
    
Using the substitution method to solve the system of equations:
5x + 2y = 14 (1)
x - 6y = 22 (2)
From equation (2), we can express x in terms of y:
x = 22 + 6y (3)
Now, substitute the expression for x from equation (3) into equation (1):
5(22 + 6y) + 2y = 14
110 + 30y + 2y = 14
32y = -96
y = -96 / 32
y = -3
Now, substitute the value of y back into equation (3) to find x:
x = 22 + 6(-3)
x = 22 - 18
x = 4
Therefore, the correct solution to the system of equations is (4, -3).
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