are there any solutions.

Question

 Draw graph to find whether the system have any solutions or not. 2x + y = 4, 6x = −3y + 6

Answer 1

First, lets get both equations in y = mx+b form.

 

Eq1

 

2x + y = 4      

 

y = -2x + 4

 

 

Eq2

 

6x = -3y + 6

 

3y = -6x + 6

 

y = -2x + 2

 

Now we draw these lines on a coordinate system.  Look for the point where these two lines intersect.  That point of intersection will be your solution.