Question 598657: :( I need help desperately, I was absent throughout this entire section :(
please help. i'm crying , i cant do it all
This is Solving substitution by elimination.
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4)
-5x+2y=-2
-7x-2y=-24
5)
-2x-y=-3
5x+y=12
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12)
y=-4x-10
y=-7x+12
13)
y=3x+14
y=-2x+4
14)
y=2x-1
2x-7y=-17
15)
y=-3x-6
7x+3y=-14
16)
3x+y=-2
-6x-y=2
17)
6x-2y=-24
7x+y=-18
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Hi, there (again)--
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The elimination method of solving systems of equations is also called the addition method. Let's solve the following system using addition/elimination.
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-5x + 2y = - 2
-7x - 2y = -24
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Note that, if we add down, the y-terms will cancel out because 2y +(-2y) = 0. We'll draw an "equals" bar under the system, and add down. (We are adding like terms together.)
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-5x + 2y = - 2
-7x - 2y = -24
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-12x = -26
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We have eliminated the y-term. Now we can divide both sides of the new equation by -12 to solve for x.
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x = (-26)/(-12)
x = 13/6
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We want to know what the y-value is when x=13/6, so we substitute 13/6 for y in one of the original equations. It doesn't matter which one we choose. Let's use the first equation since the numbers are a little smaller.
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-5x + 2y = - 2
-5*(13/6) + 2y = -2
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Now we'll simplify the equation and solve for y.
-65/6 + 2y = -2
2y = -2 + 65/6
2y = -12/6 + 65/6
2y = 53/6
y = (53/6) / 2
y = 53/12
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Using the elimination method we find that the ordered pair (x,y)=(13/6, 53/12) is the solution for this system.
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You should ALWAYS check your solution in both equations because it's quite easy to make an arithmetic error when using the elimination method.
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FIRST EQUATION:
-5x + 2y = - 2
-5*(13/6) + 2*(53/12) = -2
-65/6 + 106/12 = -2
-130/12 + 106/12 = -2
-24/12 = -2
-2 = -2
Check!
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SECOND EQUATION
-7x - 2y = -24
-7(13/6) - 2(53/12) = -24
-91/6 - 106/12 = -24
-182/12 - 106/12 = -24
-288/12 = -24
-24 = -24
Check!
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Know we know for sure that the ordered pair (x,y)=(13/6, 53/12) is the solution for this system.
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This was the simplest case of the elimination method because we add like terms in each equation with opposite signs [2y and -2y).
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Make sure you understand this solution now. Then try problem #5 yourself. It's very similar.
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As you post on algebra.com in the future, I suggest you post one, or perhaps two. problems at a time. Most tutors will provide more explanation if you do that.
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Good luck,
Ms.Figgy
math.in.the.vortex@gmail.com
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