SOLUTION: Hi!!! Solve the system using substitution y=8-x and 7=2-y I got -13=x but I can't figure out what y equals. Thank you so much!

Algebra ->  Expressions-with-variables -> SOLUTION: Hi!!! Solve the system using substitution y=8-x and 7=2-y I got -13=x but I can't figure out what y equals. Thank you so much!       Log On


   

Question 402547: Hi!!!
Solve the system using substitution
y=8-x and 7=2-y
I got -13=x but I can't figure out what y equals.
Thank you so much!
Found 3 solutions by MathLover1, Alan3354, Earlsdon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=8-x and 7=2-y
in standard form:

x%2By=8 and y=2-7=-5

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


Lets start with the given system of linear equations

1%2Ax%2B1%2Ay=8
0%2Ax%2B1%2Ay=-5

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=8-1%2AxSubtract 1%2Ax from both sides

y=%288-1%2Ax%29 Divide both sides by 1.


Which breaks down and reduces to



y=8-1%2Ax Now we've fully isolated y

Since y equals 8-1%2Ax we can substitute the expression 8-1%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


0%2Ax%2B1%2Ahighlight%28%288-1%2Ax%29%29=-5 Replace y with 8-1%2Ax. Since this eliminates y, we can now solve for x.

0%2Ax%2B1%2A%288%29%2B1%28-1%29x=-5 Distribute 1 to 8-1%2Ax

0%2Ax%2B8-1%2Ax=-5 Multiply



0%2Ax%2B8-1%2Ax=-5 Reduce any fractions

0%2Ax-1%2Ax=-5-8 Subtract 8 from both sides


0%2Ax-1%2Ax=-13 Combine the terms on the right side



-1%2Ax=-13 Now combine the terms on the left side.


cross%28%281%2F-1%29%28-1%2F1%29%29x=%28-13%2F1%29%281%2F-1%29 Multiply both sides by 1%2F-1. This will cancel out -1%2F1 and isolate x

So when we multiply -13%2F1 and 1%2F-1 (and simplify) we get



x=13 <---------------------------------One answer

Now that we know that x=13, lets substitute that in for x to solve for y

0%2813%29%2B1%2Ay=-5 Plug in x=13 into the 2nd equation

0%2B1%2Ay=-5 Multiply

1%2Ay=-5%2B0Add 0 to both sides

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

cross%28%281%2F1%29%281%29%29%2Ay=%28-5%2F1%29%281%2F1%29 Multiply both sides by 1%2F1. This will cancel out 1 on the left side.

y=-5%2F1 Multiply the terms on the right side


y=-5 Reduce


So this is the other answer


y=-5<---------------------------------Other answer


So our solution is

x=13 and y=-5

which can also look like

(13,-5)

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

1%2Ax%2B1%2Ay=8
0%2Ax%2B1%2Ay=-5

we get


graph of 1%2Ax%2B1%2Ay=8 (red) and 0%2Ax%2B1%2Ay=-5 (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 (13,-5). This verifies our answer.


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

Plug in (13,-5) into the system of equations


Let x=13 and y=-5. Now plug those values into the equation 1%2Ax%2B1%2Ay=8

1%2A%2813%29%2B1%2A%28-5%29=8 Plug in x=13 and y=-5


13-5=8 Multiply


8=8 Add


8=8 Reduce. Since this equation is true the solution works.


So the solution (13,-5) satisfies 1%2Ax%2B1%2Ay=8



Let x=13 and y=-5. Now plug those values into the equation 0%2Ax%2B1%2Ay=-5

0%2A%2813%29%2B1%2A%28-5%29=-5 Plug in x=13 and y=-5


0-5=-5 Multiply


-5=-5 Add


-5=-5 Reduce. Since this equation is true the solution works.


So the solution (13,-5) satisfies 0%2Ax%2B1%2Ay=-5


Since the solution (13,-5) satisfies the system of equations


1%2Ax%2B1%2Ay=8
0%2Ax%2B1%2Ay=-5


this verifies our answer.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
y=8-x
--------
7=2-y
5 = -y
y = -5
-------
y=8-x
-5 = 8 - x
-13 = -x
x = 13


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
1) y+=+8-x Substitute this for y in equation 2).
2) 7+=+2-y
2a) 7+=+2-%288-x%29
2b) 7+=+2-8%2Bx Notice the change of sign on x.
2c) 7+=+-6%2Bx
2d) 13+=+x or x+=+13 Notice that x is positive! Now substitute this value of x into either one of the two given equations and solve for y. Let's use equation 1).
1) y+=+8-x Substitute x = 13.
1a) y+=+8-13 so y+=+-5
The solution is: (13,-5)