Question 119835: How do you solve this system of equations where 4x+3y=-2
5x+7y=17
by using the elimination method?
Found 2 solutions by jim_thompson5910, kjwade3:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
| Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition |
Lets start with the given system of linear equations
In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).
So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.
So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 4 and 5 to some equal number, we could try to get them to the LCM.
Since the LCM of 4 and 5 is 20, we need to multiply both sides of the top equation by 5 and multiply both sides of the bottom equation by -4 like this:
 Multiply the top equation (both sides) by 5
 Multiply the bottom equation (both sides) by -4
So after multiplying we get this:
Notice how 20 and -20 add to zero (ie  )
Now add the equations together. In order to add 2 equations, group like terms and combine them
 Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.
So after adding and canceling out the x terms we're left with:
 Divide both sides by  to solve for y
 Reduce
Now plug this answer into the top equation to solve for x
 Plug in
 Multiply
 Subtract  from both sides
 Combine the terms on the right side
 Multiply both sides by  . This will cancel out  on the left side.
 Multiply the terms on the right side
So our answer is
,
which also looks like
( ,  )
Notice if we graph the equations (if you need help with graphing, check out this solver)
we get
 graph of (red) (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).
and we can see that the two equations intersect at (,). This verifies our answer. |
Answer by kjwade3(1) (Show Source):
You can put this solution on YOUR website! You can solve this two ways.
4x+3y=-2
5x+7y=17
I am going to cancel or eliminate the x's. To do this multiply both problems by a number to get the x's the same, but one positive and one negative.
5(4x+3y=-2)
-4(5x+7y=17)
You then get 20x+15y=-10
-20x-28y=-68
You subtract or add and the x's cancel or eliminate.You get -13y=-78.You divide both sides by -13 and get y=6.To get the solution for x, you plug y=6 into the original problem.
TO plug in 6, do the following
4x+3(6)=-2 which gives you 4x+18=-2.
You subtract 18 to both sides which gives you 4x=-20. YOu divide by 4 on both sides and get x=-5.
To plug in y=6 into 5x+7y=17, do the following.
5x+7(6)=17 which gives you 5x+42=17.
You subtract 42 from both sides and get 5x=-25.
You divide both sides by 5 and get x=-5
The answer is(-5,6).
THe other way to do the problems is to eliminate the y's.
4x+3y=-2
5x+7y=17
-7(4x+3y=-2)
3(5x+7y=17)
This gives you the following:
-28x-21y=14
15x+21y=51
The y's cancel or eliminate and gives you -13x=65. You divide both sides by -13 and it gives you x=-5.
Plug x=-5 back into either problem and get the solution for y. You shoud get the same answer as above which is (-5,6).
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