SOLUTION: 4x + y = 11 x + 2y = 8 Can some please explain to me how to solve the above linear equation using the substitution method? I got the answers y=3 x=2 I think I did som

Algebra ->  Linear-equations -> SOLUTION: 4x + y = 11 x + 2y = 8 Can some please explain to me how to solve the above linear equation using the substitution method? I got the answers y=3 x=2 I think I did som      Log On


   

Question 325103: 4x + y = 11
x + 2y = 8
Can some please explain to me how to solve the above linear equation using the substitution method?
I got the answers
y=3
x=2
I think I did something wrong
Found 2 solutions by jim_thompson5910, mananth:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

system%284x%2By=11%2Cx%2B2y=8%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

4x%2By=11 Start with the first equation


y=11-4x Subtract 4x from both sides


y=-4x%2B11 Rearrange the equation

---------------------

Since y=-4x%2B11, we can now replace each y in the second equation with -4x%2B11 to solve for x



x%2B2highlight%28%28-4x%2B11%29%29=8 Plug in y=-4x%2B11 into the second equation. In other words, replace each y with -4x%2B11. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B%282%29%28-4%29x%2B%282%29%2811%29=8 Distribute 2 to -4x%2B11


x-8x%2B22=8 Multiply


-7x%2B22=8 Combine like terms on the left side


-7x=8-22Subtract 22 from both sides


-7x=-14 Combine like terms on the right side


x=%28-14%29%2F%28-7%29 Divide both sides by -7 to isolate x



x=2 Divide


Since we know that x=2 we can plug it into the equation y=-4x%2B11 (remember we previously solved for y in the first equation).



y=-4x%2B11 Start with the equation where y was previously isolated.


y=-4%282%29%2B11 Plug in x=2


y=-8%2B11 Multiply


y=3 Combine like terms


So the solutions are x=2 and y=3


which form the ordered pair








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 4x%2By=11 (red) and x%2B2y=8 (green) and the intersection of the lines (blue circle).






So you have the correct answers (you probably want to say x=2 and y=3)

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
4x + y = 11......1
x + 2y = 8 ......2
..
Equation 2
x+2y=8
add -2y
x+2y-2y=8-2y
x= 8-2y
..
4x+y=11
plug the value of x in this equation
4(8-2y)+y= 11
32-8y+y=11
Add -32 to both sides
-32+32-7y=11-32
-7y=-21
y=-21/-7
y=3
..
plug the value of x in the equation x+2y=8
x+6=8
x=8-6=2
x=2