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Question 145337: Could someone please help me with a few problems on the Elimination Method?
1) 5x - y = 12
3x + y = 4
2) 2x - y = -6
2x - 2y = -4
I have the directions on how to work these problems, but I'm having a hard time understanding how to write them down on the paper.If you don't mind,would you please show me how they would look when you write them.That would help me understand it better,so when I take a test over this, I will know how it is suppose to look.
Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Jump to problem # 2
# 1
Start with the given system of equations:
Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y.
In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for  , we would have to eliminate  (or vice versa).
So lets eliminate . In order to do that, we need to have both coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.
So to make the coefficients equal in magnitude but opposite in sign, we need to multiply both coefficients by some number to get them to an common number. So if we wanted to get  and  to some equal number, we could try to get them to the LCM.
Since the LCM of and is  , we need to multiply both sides of the top equation by and multiply both sides of the bottom equation by  like this:
 Multiply the top equation (both sides) by
 Multiply the bottom equation (both sides) by
Distribute and multiply
Now add the equations together. In order to add 2 equations, group like terms and combine them
Combine like terms and simplify
 Notice how the x terms cancel out
 Simplify
 Divide both sides by  to isolate y
 Reduce
Now plug this answer into the top equation  to solve for x
Start with the first equation
 Plug in
 Multiply
 Subtract 2 from both sides
 Combine like terms on the right side
 Divide both sides by 5 to isolate x
 Divide
So our answer is
and
which also looks like )
Now let's graph the two equations (if you need help with graphing, check out this solver)
From the graph, we can see that the two equations intersect at . This visually verifies our answer.
 graph of (red) and  (green) and the intersection of the lines (blue circle).
Jump to problem # 1
# 2
Start with the given system of equations:
 Multiply the bottom equation (both sides) by  . This will allow you to cancel out the x terms.
Distribute and multiply
Now add the equations together. In order to add 2 equations, group like terms and combine them
Combine like terms and simplify
 Notice how the x terms cancel out
Simplify
Now plug this answer into the top equation to solve for x
Start with the first equation
 Plug in
 Multiply
 Subtract 2 from both sides
 Combine like terms on the right side
 Divide both sides by 2 to isolate x
 Divide
So our answer is
and
which also looks like )
Now let's graph the two equations (if you need help with graphing, check out this solver)
From the graph, we can see that the two equations intersect at . This visually verifies our answer.
 graph of (red) and  (green) and the intersection of the lines (blue circle).
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! to eliminate one of the variables, just arrange for the number value of the coefficients of the variable to be equal
__ then add or subtract the equations as needed
1) the number value (absolute value) of the y-coefficients is the same (1)
__ adding the two equations ELIMINATES the y giving 5x+3x=12+4 __ 8x=16 __ x=2
__ substituting __ 3(2)+y=4 __ 6+y=4 __ y=-2
2) the value of the x-coefficients is the same (2)
__ subtracting the 2nd equation from the 1st gives -y-(-2y)=-6-(-4) __ y=-2
__ substituting __ 2x-(-2)=-6 __ 2x=-8 __ x=-4
you can "arrange" for the coefficients to be equal by multiplying one or both of the equations by the appropriate quantities
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