SOLUTION: I need help with this math homework problem It says solve the linear equation using the substitution method: x=8-4y 3x+5y=3

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Question 145582: I need help with this math homework problem It says solve the linear equation using the substitution method:

x=8-4y
3x+5y=3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system
3x%2B5y=3
x=8-4y



3%288-4y%29%2B5y=3 Plug in x=8-4y into the first equation. In other words, replace each x with 8-4y. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


24-12y%2B5y=3 Distribute


-7y%2B24=3 Combine like terms on the left side


-7y=3-24Subtract 24 from both sides


-7y=-21 Combine like terms on the right side


y=%28-21%29%2F%28-7%29 Divide both sides by -7 to isolate y



y=3 Divide




Now that we know that y=3, we can plug this into x=8-4y to find x



x=8-4%283%29 Substitute 3 for each y


x=-4 Simplify


So our answer is x=-4 and y=3 which also looks like



Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.


+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+%283-3x%29%2F5%2C+%28x-8%29%2F%28-4%29%29+ Graph of 3x%2B5y=3 (red) and x=8-4y (green)