SOLUTION: 1.Use the Substitution method to solve the system of equations.
x + y = 10
y = x + 8
2.Use the Substitution method to solve the system of equations.
3x + y = 5
4x -
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Question 203093: 1.Use the Substitution method to solve the system of equations.
x + y = 10
y = x + 8
2.Use the Substitution method to solve the system of equations.
3x + y = 5
4x - 7y = -10
3.Use the Substitution method to solve the system of equations.
y - 2x = -5
3y - x = 5
can you please help me solve each step by step so i can under stand
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1
Start with the given system of equations:
Start with the second equation.
-------------------------------------------
Move onto the first equation.
Plug in .
Combine like terms on the left side.
Subtract from both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
-------------------------------------------
Since we know that , we can use this to find .
Go back to the second equation.
Plug in .
Add
So the solutions are and .
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)
# 2
Start with the given system of equations:
Start with the first equation.
Subtract from both sides.
Rearrange the terms and simplify.
-------------------------------------------
Move onto the second equation.
Now 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.
-------------------------------------------
Since we know that , we can use this to find .
Go back to the first equation.
Plug in .
Multiply.
Subtract from both sides.
Combine like terms on the right side.
So the solutions are and .
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)
# 3
Start with the given system of equations:
Start with the first equation.
Add to both sides.
Rearrange the terms and simplify.
-------------------------------------------
Move onto the second equation.
Now 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.
-------------------------------------------
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 .
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)
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