linear systems using the substitution method??

Question

6x=3y+2
y-2x+4=0

Answer 1

Another way to look at this:

 

Write each linear equation in the form

 

y = mx + b

 

and get

 

y = 2x - 2/3

y = 2x - 4

 

Then

 

2x - 2/3 = 2x - 4 

 

Simplify and get a false statement: 2/3 = 4

 

Hence, the system has no solution.

 

 

 

Answer 2

Since the second equation has a variable with no coefficient, let's solve it for y.

 

y - 2x + 4 = 0

y = 2x - 4

 

Now, substitute this into the first equation by replacing y with 2x - 4

 

6x = 3(2x - 4) + 2

6x = 6x - 12 + 2

6x = 6x - 10

0 ≠ -10

 

This system has no solution