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 -

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> 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 -      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


Start with the given system of equations:


system%28x%2By=10%2Cy=x%2B8%29


y=x%2B8 Start with the second equation.


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


x%2By=10 Move onto the first equation.


x%2Bx%2B8=10 Plug in y=x%2B8.


2x%2B8=10 Combine like terms on the left side.


2x=10-8 Subtract 8 from both sides.


2x=2 Combine like terms on the right side.


x=%282%29%2F%282%29 Divide both sides by 2 to isolate x.


x=1 Reduce.


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


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


y=x%2B8 Go back to the second equation.


y=1%2B8 Plug in x=1.


y=9 Add


So the solutions are x=1 and y=9.


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 x%2By=10 (red) and y=x%2B8 (green)




# 2



Start with the given system of equations:


system%283x%2By=5%2C4x-7y=-10%29


3x%2By=5 Start with the first equation.


y=5-3x Subtract 3x from both sides.


y=-3x%2B5 Rearrange the terms and simplify.


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


4x-7y=-10 Move onto the second equation.


4x-7%28-3x%2B5%29=-10 Now plug in y=-3x%2B5.


4x%2B21x-35=-10 Distribute.


25x-35=-10 Combine like terms on the left side.


25x=-10%2B35 Add 35 to both sides.


25x=25 Combine like terms on the right side.


x=%2825%29%2F%2825%29 Divide both sides by 25 to isolate x.


x=1 Reduce.


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


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


3x%2By=5 Go back to the first equation.


3%281%29%2By=5 Plug in x=1.


3%2By=5 Multiply.


y=5-3 Subtract 3 from both sides.


y=2 Combine like terms on the right side.


So the solutions are x=1 and y=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 3x%2By=5 (red) and 4x-7y=-10 (green)




# 3



Start with the given system of equations:


system%28-2x%2By=-5%2C-x%2B3y=5%29


-2x%2By=-5 Start with the first equation.


y=-5%2B2x Add 2x to both sides.


y=2x-5 Rearrange the terms and simplify.


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


-x%2B3y=5 Move onto the second equation.


-x%2B3%282x-5%29=5 Now plug in y=2x-5.


-x%2B6x-15=5 Distribute.


5x-15=5 Combine like terms on the left side.


5x=5%2B15 Add 15 to both sides.


5x=20 Combine like terms on the right side.


x=%2820%29%2F%285%29 Divide both sides by 5 to isolate x.


x=4 Reduce.


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


Since we know that x=4, we can use this to find y.


-2x%2By=-5 Go back to the first equation.


-2%284%29%2By=-5 Plug in x=4.


-8%2By=-5 Multiply.


y=-5%2B8 Add 8 to both sides.


y=3 Combine like terms on the right side.


So the solutions are x=4 and y=3.


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 -2x%2By=-5 (red) and -x%2B3y=5 (green)