SOLUTION: solve ALL using the substitution method x-3y=7 -3x+16y=28 y-2x=0 3x+7y=17 r-2s=0 4r-3s=15 3b+2a=2 -2b+a=8

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: solve ALL using the substitution method x-3y=7 -3x+16y=28 y-2x=0 3x+7y=17 r-2s=0 4r-3s=15 3b+2a=2 -2b+a=8      Log On


   

Question 207645: solve ALL using the substitution method
x-3y=7
-3x+16y=28

y-2x=0
3x+7y=17

r-2s=0
4r-3s=15

3b+2a=2
-2b+a=8
Found 2 solutions by jim_thompson5910, rfer:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you going in the right direction.


# 1

x-3y=7 Start with the first equation.


x=3y%2B7 Add 3y to both sides.


-3x%2B16y=28 Move onto the second equation


-3%283y%2B7%29%2B16y=28 Plug in x=3y%2B7


-9y-21%2B16y=28 Distribute.


7y-21=28 Combine like terms on the left side.


7y=28%2B21 Add 21 to both sides.


7y=49 Combine like terms on the right side.


y=%2849%29%2F%287%29 Divide both sides by 7 to isolate y.


y=7 Reduce.


x=3y%2B7 Go back to the first isolated equation.


x=3%287%29%2B7 Plug in y=7


x=21%2B7 Multiply.


x=28 Combine like terms.


So the solutions are x=28 and y=7 which form the ordered pair (28,7)


This means that the system is consistent and independent.




# 2

-2x%2By=0 Start with the first equation.


y=2x Add 2x to both sides.


3x%2B7y=17 Move onto the second equation.


3x%2B7%282x%29=17 Plug in y=2x.


3x%2B14x=17 Multiply.


17x=17 Combine like terms on the left side.


x=%2817%29%2F%2817%29 Divide both sides by 17 to isolate x.


x=1 Reduce.


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


Since we know that x=1, we can use this to find y.


y-2x=0 Go back to the first equation.


y-2%281%29=0 Plug in x=1.


y-2=0 Multiply.


y=0%2B2 Add 2 to both sides.


y=2 Combine like terms on the right side.


So the solutions are x=1 and y=2 which form the ordered pair (1,2)


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of y-2x=0 (red) and 3x%2B7y=17 (green)

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
A)
x-3y=7, x=3y+7
-------------
-3x+16y=28
-3(3y+7)+16y=28
-9y-21+16y=28
7y=49
y=7
------------------
x-3y=7
x-3(7)=7
x-21=7
x=28
------------------
-3(28)+16(7)=28
-84+112=28
You try the others
Good luck
Bob