SOLUTION: Solve the following system of equations using substitution and elimination. Please include step by step line by line explanations 3x+y=9 9x+3y=12

Algebra ->  Linear-equations -> SOLUTION: Solve the following system of equations using substitution and elimination. Please include step by step line by line explanations 3x+y=9 9x+3y=12       Log On


   

Question 1140938: Solve the following system of equations using substitution and elimination. Please include step by step line by line explanations
3x+y=9
9x+3y=12
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
system%283x%2By=9%2C9x%2B3y=12%29

At least simplify the second equation, division by 3 both sides:

system%283x%2By=9%2C3x%2By=4%29
Next, regardless of substitution or elimination method, these are two parallel lines so NO SOLUTION for the system.

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Look! Simplifying the second equation gives you two equations representing lines WITH THE SAME SLOPE. The lines will be parallel and do NOT intersect.
NO SOLUTION!


Still not satisfied? Try substitution. Take first equation and solve for y in terms of x.
y=-3x%2B9
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The second equation of the system was already simplifiable to 3x%2By=4. Now substitute for y:
3x%2B%28-3x%2B9%29=4
3x-3x%2B9=4
9=4
Do you see a contradiction here? Did you find a solution for the variable, x?
NO SOLUTION