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how do you solve 4x - y = 5 and 4x + 4y =-4 using elimination

Please solve the linear system using elimination.
 
                             4x - y = 5
                             4x + 4y = -4
 
Please show steps.
 
Thanks
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3 Answers

Hi L;
Elimination means we have to eliminate the x or y initially, and then proceed to solve.
4x - y = 5
4x + 4y = -4
 
Let's note that 4x is in both equations.
Let's subtract the second equation from the first.  We could do the first equation from the second.  I randomly select the first arrangement...
4x - y = 5
-(4x + 4y = -4)
0-5y=9
-5y=9
y=-9/5
 
We eliminated x and solved for y.  Now, let solve for x by plugging-in y=-9/5.  I randomly select the first equation...
4x - y = 5
4x-(-9/5)=5
4x+(9/5)=5
Let's eliminate the fraction.  Let's multiply both sides by 5...
5[4x+(9/5)]=(5)(5)
20x+9=25
20x=16
x=16/20
x=4/5
 
Let's verify with the second equation...
4x + 4y = -4
[4(4/5)]+[4(-9/5)]=-4
(16/5)-(36/5)=-4
5[(16/5)-(36/5)]=(-4)(5)
16-36=-20
-20=-20
It works!!!!
Hey there, L. Let's walk through this problem step-by-step.
 
  1. So you have two equations, each with an x and a y. We need to get one variable to stand alone in one equation so that we can plug it back into the other equation to solve for one variable. Then we can solve for the second. So we have   4x - y = 5 and 4x + 4y = -4. I would go ahead and simplify the second equation by dividing every term by 4. That is, (4x/4) + (4y/4) = (-4/4), so x + y = -1. 
  2. Let's take the first equation,  4x - y = 5, and get y by itself. We add y to both sides to get 4x = 5 + y. Then we subtract 5 from both sides to get y = 4x - 5. 
  3. Plug that "y" into our second, simplified equation, x + y = - 1. If y = 4x - 5, simply plug it in to get "x + 4x - 5 = -1"
  4. You simplify x + 4x - 5 = -1 by adding like terms, so you get 5x - 5 = -1. Adding 5 to both sides gives you 5x = 4. Divide both sides by 5 gives you x = 4/5.
  5. Now you can plug that x = 4/5 into either equation to find y. Let's use our simplified x + y = -1. We now have 4/5 + y = -1. Subtract 4/5 from both sides to get that y = -1 and 4/5, or - 9/5. 
  6. Therefore, x = 4/5 and y = -9/5. 
  7. You can check this by plugging x and y into both equations. 
 Just like any other, by elimination method
 
      4x - Y = 5
   - (4X + 4Y = -4 )
     
       3 Y =  9      Y = 3  / Subtract 2nd equation from the first)
 
     Substitute back into 1st   equation to find x.  

Comments

I am confused.  If  I put 3 for y then the first equation I get 2 for x.  4(2) - 3 = 5.  But when I use the same for the 2nd equation, it doesn't work.  I get a positive 4 for the answer.
 
-4(2) + 4(3) = 4.   Equation 2's answer is a -4.
Actually, this one was done in a heap of hurry. The SECOND equation should have been written as
 
-4x -4y = +4
 
Then when you add I and II together, you get -5y = 9  or y = - 9/5
You have to Substitute in :4X + 4y = -4 
 
    To get the answer.
 
      The whole 2nd equation was multiplied   by -1 to subtracted from the first equation.
      You used substitution by only multiplying the first term 4X by -1. 

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