Question 141088: 3x+4y=17
6y-2x=-20
Im stuck.
Found 2 solutions by jim_thompson5910, rapaljer:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
 Start with the second equation
 Rearrange the terms
So now we have the system of equations:
Let's use elimination to solve this system
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
 Add 4 to both sides
 Combine like terms on the right side
 Divide both sides by 3 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 rapaljer(4671)  (Show Source):
You can put this solution on YOUR website! 3x+4y=17
6y-2x=-20
Rewrite this as
3x+4y=17
-2x + 6y=-20
To eliminate the x terms, you need to find a "common number" between the x coefficients. This would be 6. Multiply both sides of the first equation by 2 and the second equation by 3, and the x terms will subtract out!
2(3x+4y)=2(17)
3(-2x + 6y)=3(-20)
6x+8y=34
-6x +18y = -60
26y = -26
y=-1
Solve for x by substituting the value of y =-1 into the first equation:
3x+4y=17
3x+4(-1) = 17
3x -4=17
3x=21
x=7
Check by substituting both values into the second equation:
-2x + 6y=-20
-2(7) + 6(-1) =-20
-14-6=-20
This checks!!
For additional explanation on the topic of Systems of Equatiaons, see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take the second link on my homepage which is "Basic, Intermediate, and College Algebra: One Step at a Time", click on "Basic Algebra" and look for Chapter 4, Section 4.07. This is an explanation written for folks who didn't get math the first time!!
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