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
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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) (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
Start with the first equation.
Add 3y to both sides.
Move onto the second equation
Plug in
Distribute.
Combine like terms on the left side.
Add to both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
Go back to the first isolated equation.
Plug in
Multiply.
Combine like terms.
So the solutions are and which form the ordered pair (28,7)
This means that the system is consistent and independent.
# 2
Start with the first equation.
Add to both sides.
Move onto the second equation.
Plug in .
Multiply.
Combine like terms on the left side.
Divide both sides by to isolate .
Reduce.
-------------------------------------------
Since we know that , we can use this to find .
Go back to the first equation.
Plug in .
Multiply.
Add to both sides.
Combine like terms on the right side.
So the solutions are and 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 (red) and (green)
Answer by rfer(16322) (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
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