The following system of equations is _____.
y = -1/3x +2/3
2x + 6y = 4
is it equivalent, consistent, or inconsistent?
system of equations in math?
2008-09-11 4:16 pm
回答 (5)
2008-09-11 4:22 pm
✔ 最佳答案
2x + 6( -1/3x +2/3 ) = 4 2x (-2x+4)=4
-4x^2+8x-4=0
-x^2+2x-4=0
no roots
2008-09-11 11:28 pm
First, subtract 2x from both sides of equation #2:
6y = -2x + 4
Next, divide both sides by 6:
y = -(2/6)x + 4/6
Finally. simplify it:
y = -(1/3)x + 2/3
The two equations are equivalent.
6y = -2x + 4
Next, divide both sides by 6:
y = -(2/6)x + 4/6
Finally. simplify it:
y = -(1/3)x + 2/3
The two equations are equivalent.
2008-09-11 11:27 pm
Multiply equation (1) by 3
3y =-x + 2
-x+3y =2 -------(1)
2x+6y=4 -------(2)
Multiply equation (1) by 2 and add
-2x+6y=4
2x+6y=4
12y=8
y=8/12=2/3
plug this y into (2)
2x+6(2/3)=4
2x+4=4
x=0
consistent
3y =-x + 2
-x+3y =2 -------(1)
2x+6y=4 -------(2)
Multiply equation (1) by 2 and add
-2x+6y=4
2x+6y=4
12y=8
y=8/12=2/3
plug this y into (2)
2x+6(2/3)=4
2x+4=4
x=0
consistent
2008-09-11 11:25 pm
y = -1/3(x) + 2/3 (solve by using substitution)
2x + 6y = 4
2x + 6y = 4
2x + 6(-x/3 + 2/3) = 4
2x + (-2x) + 4 = 4
2x - 2x + 4 = 4
2x - 2x = 4 - 4
0 = 0
(they are the same line)
(infinite solutions)
â´ it is equivalent.
2x + 6y = 4
2x + 6y = 4
2x + 6(-x/3 + 2/3) = 4
2x + (-2x) + 4 = 4
2x - 2x + 4 = 4
2x - 2x = 4 - 4
0 = 0
(they are the same line)
(infinite solutions)
â´ it is equivalent.
2008-09-11 11:25 pm
First of all simplify the eqauitions
first equation needs to be multiplied by three to get rid of the fractions
and divide the second one by 2
3y = - x + 2
x + 3y = 2
transfer the x varible of the first equation
x + 3y = 2
This tells you that it is equivalent.
first equation needs to be multiplied by three to get rid of the fractions
and divide the second one by 2
3y = - x + 2
x + 3y = 2
transfer the x varible of the first equation
x + 3y = 2
This tells you that it is equivalent.
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