SOLUTION: Systems of equations: find the solution to the system equations: 3/2y-5=x 3y-2x=12 Can you please help me step-by-step

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Question 149176: Systems of equations:


find the solution to the system equations:
3/2y-5=x
3y-2x=12
Can you please help me step-by-step
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.%283%2F2%29y-5=x
2.3y-2x=12
You can solve a system of linear equations by the substitution method.
You subsitute an expression for one variable from one equation into the other equation.
Eq. 1 is an expression for x in terms of y.
Substitute this term for x in eq. 2 and solve for y.
3y-2x=12
3y-2%28%283%2F2%29y-5%29=12
3y-3y%2B10=12
10=12
Well that's not true.
Your equations have led to a statement that is not true.
Your system of linear equations is inconsistent and there is no solution.
If you look at the system of equations graphically, it's clearer what's going on.
First put the equation into slope intercept form, then graph.
1.%283%2F2%29y-5=x
%283%2F2%29y=x%2B5
y=%282%2F3%29%28x%2B5%29
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+%282%2F3%29%2A%28x%2B5%29%29+
2.3y-2x=12
3y=2x%2B12
y=%282x%2B12%29%2F3

You see that the lines are parallel.
That means, there is no point (x,y) where they meet.
There is no solution.