SOLUTION: hi, please help me solve this problem ( solve the linear system using subsitution) y-2x=-6. 5x-y=9 thank you

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Question 404598: hi, please help me solve this problem ( solve the linear system using subsitution) y-2x=-6. 5x-y=9
thank you
Found 2 solutions by MathLover1, ewatrrr:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y-2x=-6.....or -2x+%2B+y+=-6
+5x-y=9

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


Lets start with the given system of linear equations

-2%2Ax%2B1%2Ay=-6
5%2Ax-1%2Ay=9

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=-6%2B2%2AxAdd 2%2Ax to both sides

y=%28-6%2B2%2Ax%29 Divide both sides by 1.


Which breaks down and reduces to



y=-6%2B2%2Ax Now we've fully isolated y

Since y equals -6%2B2%2Ax we can substitute the expression -6%2B2%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


5%2Ax%2B-1%2Ahighlight%28%28-6%2B2%2Ax%29%29=9 Replace y with -6%2B2%2Ax. Since this eliminates y, we can now solve for x.

5%2Ax-1%2A%28-6%29-1%282%29x=9 Distribute -1 to -6%2B2%2Ax

5%2Ax%2B6-2%2Ax=9 Multiply



5%2Ax%2B6-2%2Ax=9 Reduce any fractions

5%2Ax-2%2Ax=9-6 Subtract 6 from both sides


5%2Ax-2%2Ax=3 Combine the terms on the right side



3%2Ax=3 Now combine the terms on the left side.


cross%28%281%2F3%29%283%2F1%29%29x=%283%2F1%29%281%2F3%29 Multiply both sides by 1%2F3. This will cancel out 3%2F1 and isolate x

So when we multiply 3%2F1 and 1%2F3 (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

5%281%29-1%2Ay=9 Plug in x=1 into the 2nd equation

5-1%2Ay=9 Multiply

-1%2Ay=9-5Subtract 5 from both sides

-1%2Ay=4 Combine the terms on the right side

cross%28%281%2F-1%29%28-1%29%29%2Ay=%284%2F1%29%281%2F-1%29 Multiply both sides by 1%2F-1. This will cancel out -1 on the left side.

y=4%2F-1 Multiply the terms on the right side


y=-4 Reduce


So this is the other answer


y=-4<---------------------------------Other answer


So our solution is

x=1 and y=-4

which can also look like

(1,-4)

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

-2%2Ax%2B1%2Ay=-6
5%2Ax-1%2Ay=9

we get


graph of -2%2Ax%2B1%2Ay=-6 (red) and 5%2Ax-1%2Ay=9 (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,-4). This verifies our answer.


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

Plug in (1,-4) into the system of equations


Let x=1 and y=-4. Now plug those values into the equation -2%2Ax%2B1%2Ay=-6

-2%2A%281%29%2B1%2A%28-4%29=-6 Plug in x=1 and y=-4


-2-4=-6 Multiply


-6=-6 Add


-6=-6 Reduce. Since this equation is true the solution works.


So the solution (1,-4) satisfies -2%2Ax%2B1%2Ay=-6



Let x=1 and y=-4. Now plug those values into the equation 5%2Ax-1%2Ay=9

5%2A%281%29-1%2A%28-4%29=9 Plug in x=1 and y=-4


5%2B4=9 Multiply


9=9 Add


9=9 Reduce. Since this equation is true the solution works.


So the solution (1,-4) satisfies 5%2Ax-1%2Ay=9


Since the solution (1,-4) satisfies the system of equations


-2%2Ax%2B1%2Ay=-6
5%2Ax-1%2Ay=9


this verifies our answer.

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


Hi

solving the linear system using substitution

y-2x=-6   | y = (2x-6)

5x-y = 9

5x -(2x-6) = 9  |substituting for y

solving for x

  3x +6 =  9

    3x = 3

     x = 1     y = -4   (2x-6)

CHECKING our Answer***

y-2x= -6 

-4-2= -6