SOLUTION: Hi I would like to ask you how to get Y by itself in this system of equation 4x -1y = -1 x + 1y = -4 Please be detailed I do not have a clue into getting y by itself please

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Hi I would like to ask you how to get Y by itself in this system of equation 4x -1y = -1 x + 1y = -4 Please be detailed I do not have a clue into getting y by itself please      Log On


   

Question 684301: Hi I would like to ask you how to get Y by itself in this system of equation
4x -1y = -1
x + 1y = -4
Please be detailed I do not have a clue into getting y by itself please help!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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


Lets start with the given system of linear equations

4%2Ax-1%2Ay=-1
1%2Ax%2B1%2Ay=-4

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

-1%2Ay=-1-4%2AxSubtract 4%2Ax from both sides

y=%28-1-4%2Ax%29%2F-1 Divide both sides by -1.


Which breaks down and reduces to



y=1%2B4%2Ax Now we've fully isolated y

Since y equals 1%2B4%2Ax we can substitute the expression 1%2B4%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


1%2Ax%2B1%2Ahighlight%28%281%2B4%2Ax%29%29=-4 Replace y with 1%2B4%2Ax. Since this eliminates y, we can now solve for x.

1%2Ax%2B1%2A%281%29%2B1%284%29x=-4 Distribute 1 to 1%2B4%2Ax

1%2Ax%2B1%2B4%2Ax=-4 Multiply



1%2Ax%2B1%2B4%2Ax=-4 Reduce any fractions

1%2Ax%2B4%2Ax=-4-1 Subtract 1 from both sides


1%2Ax%2B4%2Ax=-5 Combine the terms on the right side



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


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

So when we multiply -5%2F1 and 1%2F5 (and simplify) we get



x=-1 <---------------------------------One answer

Now that we know that x=-1, lets substitute that in for x to solve for y

1%28-1%29%2B1%2Ay=-4 Plug in x=-1 into the 2nd equation

-1%2B1%2Ay=-4 Multiply

1%2Ay=-4%2B1Add 1 to both sides

1%2Ay=-3 Combine the terms on the right side

cross%28%281%2F1%29%281%29%29%2Ay=%28-3%2F1%29%281%2F1%29 Multiply both sides by 1%2F1. This will cancel out 1 on the left side.

y=-3%2F1 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=-1 and y=-3

which can also look like

(-1,-3)

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

4%2Ax-1%2Ay=-1
1%2Ax%2B1%2Ay=-4

we get


graph of 4%2Ax-1%2Ay=-1 (red) and 1%2Ax%2B1%2Ay=-4 (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 (-1,-3). This verifies our answer.


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Check:

Plug in (-1,-3) into the system of equations


Let x=-1 and y=-3. Now plug those values into the equation 4%2Ax-1%2Ay=-1

4%2A%28-1%29-1%2A%28-3%29=-1 Plug in x=-1 and y=-3


-4%2B3=-1 Multiply


-1=-1 Add


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


So the solution (-1,-3) satisfies 4%2Ax-1%2Ay=-1



Let x=-1 and y=-3. Now plug those values into the equation 1%2Ax%2B1%2Ay=-4

1%2A%28-1%29%2B1%2A%28-3%29=-4 Plug in x=-1 and y=-3


-1-3=-4 Multiply


-4=-4 Add


-4=-4 Reduce. Since this equation is true the solution works.


So the solution (-1,-3) satisfies 1%2Ax%2B1%2Ay=-4


Since the solution (-1,-3) satisfies the system of equations


4%2Ax-1%2Ay=-1
1%2Ax%2B1%2Ay=-4


this verifies our answer.