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

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

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

Start with the first equation

Subtract from both sides

Rearrange the equation

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

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 22 from both sides

Combine like terms on the right side

Divide both sides by -7 to isolate x

Divide

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

So the solutions are and

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 (red) and (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) (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
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