SOLUTION: Solving for Two Variables using Elimination 8x + 6y = 4 and -8x + 5y = 62

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Question 1180168: Solving for Two Variables using Elimination
8x + 6y = 4 and -8x + 5y = 62
Found 4 solutions by mananth, MathLover1, ankor@dixie-net.com, ewatrrr:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

8x + 6y = 4
-8x + 5y = 62
Add both equations
we get 11y =66
y=6
Plug value of y in the equation
8x + 6y = 4
8x+36=4
8x=-32
x=-4

Answer by MathLover1(20850) About Me  (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

8%2Ax%2B6%2Ay=4
-8%2Ax%2B5%2Ay=62

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 8 and -8 to some equal number, we could try to get them to the LCM.

Since the LCM of 8 and -8 is -8, we need to multiply both sides of the top equation by -1 and multiply both sides of the bottom equation by -1 like this:

-1%2A%288%2Ax%2B6%2Ay%29=%284%29%2A-1 Multiply the top equation (both sides) by -1
-1%2A%28-8%2Ax%2B5%2Ay%29=%2862%29%2A-1 Multiply the bottom equation (both sides) by -1


So after multiplying we get this:
-8%2Ax-6%2Ay=-4
8%2Ax-5%2Ay=-62

Notice how -8 and 8 add to zero (ie -8%2B8=0)


Now add the equations together. In order to add 2 equations, group like terms and combine them
%28-8%2Ax%2B8%2Ax%29-6%2Ay-5%2Ay%29=-4-62

%28-8%2B8%29%2Ax-6-5%29y=-4-62

cross%28-8%2B8%29%2Ax%2B%28-6-5%29%2Ay=-4-62 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:

-11%2Ay=-66

y=-66%2F-11 Divide both sides by -11 to solve for y



y=6 Reduce


Now plug this answer into the top equation 8%2Ax%2B6%2Ay=4 to solve for x

8%2Ax%2B6%286%29=4 Plug in y=6


8%2Ax%2B36=4 Multiply



8%2Ax=4-36 Subtract 36 from both sides

8%2Ax=-32 Combine the terms on the right side

cross%28%281%2F8%29%288%29%29%2Ax=%28-32%29%281%2F8%29 Multiply both sides by 1%2F8. This will cancel out 8 on the left side.


x=-4 Multiply the terms on the right side


So our answer is

x=-4, y=6

which also looks like

(-4, 6)

Notice if we graph the equations (if you need help with graphing, check out this solver)

8%2Ax%2B6%2Ay=4
-8%2Ax%2B5%2Ay=62

we get



graph of 8%2Ax%2B6%2Ay=4 (red) -8%2Ax%2B5%2Ay=62 (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 (-4,6). This verifies our answer.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solving for Two Variables using Elimination
8x + 6y = 4
-8x + 5y = 62
----------------addition eliminates x, find y
0 + 11y = 66
y = 66/11
y = 6
:
find x using the 1st equation, replace y with 6
8x + 6(6) = 4
8x + 36 = 4
8x = 4 - 36
x = -32/8
x = -4
:
:
Check in the 2nd equation
-8(-4) + 5(6) = 62
+32 + 30 = 62

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
  8x + 6y = 4      and    
 -8x + 5y = 62
11y = 66
  y = 6   and x = -4  8x+=+-32%29
 P(-4, 6) the solution for this system of equations
Wish You the Best in your Studies.
y= (-4/3)x +.5  and y = (8/5)x + 62/5