Okay, first off I am home schooled and I teach myself... That means if my book doesn't explain anything, I don't have much choice but to ask someone else.
Anyway, this system of equations has been giving me some problems:
First: 4x-2y=2
Second: y=-4x-7
I have tried solving it using graphing and algebraically, I just can't seem to find a exact solution. I don't know if my math is wrong or what, but my book asks the question as if it can't be inconsistent.
Any help would be great, just as long as there is an explanation.
I need help with a system of equations.?
2008-09-16 2:35 pm
回答 (9)
2008-09-16 2:42 pm
✔ 最佳答案
OK Since you have the second in the form of y = , use substitution
First: 4x-2y=2
Second: y=-4x-7; so
4x - 2(-4x-7) = 2
4x +8x +14 = 2
12x + 14 = 2
12x = -12
x = -1
Substitute back
y = -4(-1) -7
y = 4 -7
y = -3
Prove by placing both in the first equation
4(-1) -2(-3) = 2 ??
-4 + 6 = 2 ??
2 = 2 YES!!!
Hope that helps.
2008-09-16 2:50 pm
If y = 4x - 7,
then, you can take what's to the right of the equal sign and substitute for y in the other equation.
4x - 2 (-4x - 7) = 2
Multiply -2 by each of the terms inside the parenthesis
4x + 8x + 14 = 2
Simplify
12x + 14 = 2
12x = 2 - 14
12x = -12
Divide both sides of the equation by -12
12/-12 x = -12 /-12 x
-x = 1
x = -1
Now that you know that x = -1, substitute x with -1 on EITHER equation
y = -4x - 7
y = -4(-1) - 7
y = 4 -7
y = -3
then, you can take what's to the right of the equal sign and substitute for y in the other equation.
4x - 2 (-4x - 7) = 2
Multiply -2 by each of the terms inside the parenthesis
4x + 8x + 14 = 2
Simplify
12x + 14 = 2
12x = 2 - 14
12x = -12
Divide both sides of the equation by -12
12/-12 x = -12 /-12 x
-x = 1
x = -1
Now that you know that x = -1, substitute x with -1 on EITHER equation
y = -4x - 7
y = -4(-1) - 7
y = 4 -7
y = -3
2008-09-16 2:50 pm
4x-2y=2}
y=-4x-7 } try firstly to leave only y in the first part in the first equation.So...
-2y=-4x+2}
y=-4X-7} now let's divide both part of the first equation with -2.So...
y=2x-1}
y=-4x-7} now the first part are equal and so do the second(y=y)So...
2x-1=-4x-7 we separate the x and the numbers in each part and...
2x+4x=1-7 and 6x=-6 so...x=-1
by putting in one of the equations above where x , -1 we have that y=-3
y=-4x-7 } try firstly to leave only y in the first part in the first equation.So...
-2y=-4x+2}
y=-4X-7} now let's divide both part of the first equation with -2.So...
y=2x-1}
y=-4x-7} now the first part are equal and so do the second(y=y)So...
2x-1=-4x-7 we separate the x and the numbers in each part and...
2x+4x=1-7 and 6x=-6 so...x=-1
by putting in one of the equations above where x , -1 we have that y=-3
2008-09-16 2:44 pm
substitute the entire second equation for Y in the first equation.
4x- 2(-4x-7) = 2
4x+8x+14 = 2
12x + 14 = 2
12x = -12
x = -1
now use that value of x in the equation that would be easier for you to solve
Y = -4(-1) - 7
Y = 4-7
Y= -3
answer: (-1, -3)
4x- 2(-4x-7) = 2
4x+8x+14 = 2
12x + 14 = 2
12x = -12
x = -1
now use that value of x in the equation that would be easier for you to solve
Y = -4(-1) - 7
Y = 4-7
Y= -3
answer: (-1, -3)
2008-09-16 2:43 pm
Since you know from the 2nd equation that y = -4x - 7, put that y into the 1st equation:
4x - 2(-4x - 7) = 2
4x + 8x + 14 = 2
12x + 14 = 2
12x = -12
x = -1
Put that x into the 2nd equation:
y = -4x - 7 = -4*(-1) - 7 = 4 - 7 = -3
4x - 2(-4x - 7) = 2
4x + 8x + 14 = 2
12x + 14 = 2
12x = -12
x = -1
Put that x into the 2nd equation:
y = -4x - 7 = -4*(-1) - 7 = 4 - 7 = -3
2008-09-16 2:41 pm
take the first equation:
4x-2y=2 -> 2x - y = 1
But from the second equation y = -4x - 7
so 2x - y = 1 -> 2x - (-4x - 7) = 1
2x + 4x + 7 = 1
6x = -6, x = -1
y = -4x - 7 = 4 - 7 = -3
4x-2y=2 -> 2x - y = 1
But from the second equation y = -4x - 7
so 2x - y = 1 -> 2x - (-4x - 7) = 1
2x + 4x + 7 = 1
6x = -6, x = -1
y = -4x - 7 = 4 - 7 = -3
2008-09-16 2:40 pm
4x - 2(- 4x - 7) = 2
4x + 8x + 14 = 2
12x = - 12
x = - 1
y = 4 - 7
y = - 3
x = - 1 , y = - 3
4x + 8x + 14 = 2
12x = - 12
x = - 1
y = 4 - 7
y = - 3
x = - 1 , y = - 3
2016-11-29 5:02 pm
the place to start is to locate the thank you to integrate the two equations into one ideally removing between the unknowns interior the technique. So: x-y=3 would be rearranged to x=3+y Substituting this into the 1st equation supplies (3+y)squared + y squared = 29 remedy this to get an answer for y then replace this variety for y interior the 2nd equation and remedy to get x. answer: y = 2 x = 5
2008-09-16 3:23 pm
4x - 2y = 2 (solve by using substitution)
y = -4x - 7
4x - 2y = 2
4x - 2(-4x - 7) = 2
4x + 8x + 14 = 2
12x = 2 - 14
12x = -12
x = -12/12
x = -1
4x - 2y = 2
4(-1) - 2y = 2
-2y = 2 + 4
-2y = 6
y = 6/-2
y = -3
∴ x = -1 , y = -3
y = -4x - 7
4x - 2y = 2
4x - 2(-4x - 7) = 2
4x + 8x + 14 = 2
12x = 2 - 14
12x = -12
x = -12/12
x = -1
4x - 2y = 2
4(-1) - 2y = 2
-2y = 2 + 4
-2y = 6
y = 6/-2
y = -3
∴ x = -1 , y = -3
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