SOLUTION: Solve the system by addition or substitution. –6x + 3y = 12 y = 2x + 3

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Question 82523: Solve the system by addition or substitution.
–6x + 3y = 12
y = 2x + 3

Found 2 solutions by ptaylor, tutorcecilia:
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system by addition or substitution.
–6x + 3y = 12-------------------------------eq1
y = 2x + 3 ---------------------------eq2
We'll us substitution to solve:
substitute y=2x+3 from eq2 into eq1 and we have:
-6x+3(2x+3)=12 get rid of parens
-6x+6x+9=12 No solution--------------Why???????????
First, let's examine eq1
-6x+3y=12 add 6x to both sides
-6x+6x+3y=6x+12 collect like terms
+3y=6x+12 divide both sides by 3
y=2x+4-----------------------------the revised eq1
Compare the slope of eq1 with the slope of eq2
If you plot eq1 and eq2, you will be able to see why there is no solution.
Hope this helps---ptaylor

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
–6x + 3y = 12 [re=write]
-6x+6x+3y=6x+12
3y=6x+12
3y/3=6x/3+12/3
y=2x+4
.
y=2x+4
y=2x+3
______
.
.
(-1)y=2x+4
y=2x+3
______
.
.
-y=-2=-4
y=2x+3
________
0y=0x+-1
o=-1 [untrue statement, so there is no solution or no points in common]
.
Also, note that the lines have the same slope (2), therefore the lines are parallel and will never intersect.