SOLUTION: Can you help me with this problem? Solve for x. x+2y= -1 3x-4y= 27 I think I am supposed to solve for y in one problem, then subst

Algebra ->  Expressions-with-variables -> SOLUTION: Can you help me with this problem? Solve for x. x+2y= -1 3x-4y= 27 I think I am supposed to solve for y in one problem, then subst      Log On


   

Question 93319: Can you help me with this problem? Solve for x. x+2y= -1
3x-4y= 27
I think I am supposed to solve for y in one problem, then substitute it in the next one... but I'm not sure. Thanks in advance!!!
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x.
1st: x+2y= -1
2nd: 3x-4y= 27
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Solve 1st for x:
x = -2y-1
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Substitute that into 2nd and solve for y:
3(-2y-1) - 4y = 27
-6y-3 -4y = 27
-10y = 30
y = -3
--------------
Substitute that into x = -2y-1 and solve for x:
x = -2*-3-1
x = 5
--------------
System solution:
x=5; y=-3
================
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to solve this system using substitution right?


Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

1%2Ax%2B2%2Ay=-1
3%2Ax-4%2Ay=27

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

Solve for y for the first equation

2%2Ay=-1-1%2AxSubtract 1%2Ax from both sides

y=%28-1-1%2Ax%29%2F2 Divide both sides by 2.


Which breaks down and reduces to



y=-1%2F2-%281%2F2%29%2Ax Now we've fully isolated y

Since y equals -1%2F2-%281%2F2%29%2Ax we can substitute the expression -1%2F2-%281%2F2%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


3%2Ax%2B-4%2Ahighlight%28%28-1%2F2-%281%2F2%29%2Ax%29%29=27 Replace y with -1%2F2-%281%2F2%29%2Ax. Since this eliminates y, we can now solve for x.

3%2Ax-4%2A%28-1%2F2%29-4%28-1%2F2%29x=27 Distribute -4 to -1%2F2-%281%2F2%29%2Ax

3%2Ax%2B4%2F2%2B%284%2F2%29%2Ax=27 Multiply



3%2Ax%2B2%2B2%2Ax=27 Reduce any fractions

3%2Ax%2B2%2Ax=27-2 Subtract 2 from both sides


3%2Ax%2B2%2Ax=25 Combine the terms on the right side



5%2Ax=25 Now combine the terms on the left side.


cross%28%281%2F5%29%285%2F1%29%29x=%2825%2F1%29%281%2F5%29 Multiply both sides by 1%2F5. This will cancel out 5%2F1 and isolate x

So when we multiply 25%2F1 and 1%2F5 (and simplify) we get



x=5 <---------------------------------One answer

Now that we know that x=5, lets substitute that in for x to solve for y

3%285%29-4%2Ay=27 Plug in x=5 into the 2nd equation

15-4%2Ay=27 Multiply

-4%2Ay=27-15Subtract 15 from both sides

-4%2Ay=12 Combine the terms on the right side

cross%28%281%2F-4%29%28-4%29%29%2Ay=%2812%2F1%29%281%2F-4%29 Multiply both sides by 1%2F-4. This will cancel out -4 on the left side.

y=12%2F-4 Multiply the terms on the right side


y=-3 Reduce


So this is the other answer


y=-3<---------------------------------Other answer


So our solution is

x=5 and y=-3

which can also look like

(5,-3)

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

1%2Ax%2B2%2Ay=-1
3%2Ax-4%2Ay=27

we get


graph of 1%2Ax%2B2%2Ay=-1 (red) and 3%2Ax-4%2Ay=27 (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.


and we can see that the two equations intersect at (5,-3). This verifies our answer.


-----------------------------------------------------------------------------------------------
Check:

Plug in (5,-3) into the system of equations


Let x=5 and y=-3. Now plug those values into the equation 1%2Ax%2B2%2Ay=-1

1%2A%285%29%2B2%2A%28-3%29=-1 Plug in x=5 and y=-3


5-6=-1 Multiply


-1=-1 Add


-1=-1 Reduce. Since this equation is true the solution works.


So the solution (5,-3) satisfies 1%2Ax%2B2%2Ay=-1



Let x=5 and y=-3. Now plug those values into the equation 3%2Ax-4%2Ay=27

3%2A%285%29-4%2A%28-3%29=27 Plug in x=5 and y=-3


15%2B12=27 Multiply


27=27 Add


27=27 Reduce. Since this equation is true the solution works.


So the solution (5,-3) satisfies 3%2Ax-4%2Ay=27


Since the solution (5,-3) satisfies the system of equations


1%2Ax%2B2%2Ay=-1
3%2Ax-4%2Ay=27


this verifies our answer.