Determine whether there is a solution for the system of linear equations below. If not, explain why not.
y= 3x+1
3y+2=6x-1

Please help!

Question

Determine whether there is a solution for the system of linear equations below. If not, explain why not.
y= 3x+1
3y+2=6x-1

Please help!

callisto · Answer

Put y= 3x+1 into 3y+2=6x-1
3 (3x+1 ) +2 = 6x -1

Expand the terms and simplify it
3(3x) +1(3) +2 =6x -1
9x +3+2 =6x -1
9x +5 = 6x -1

minus 6x on both sides and minus 5 on both sides

9x +5 = 6x -1
9x +5 -6x -5 = 6x-1 -6x -5
Simplify it
3x = -6
Divide both sides by -3 and you can get a value of x
Since there is a solution to the equation, they have a intersection point

So do you understand it?

anonymous · Answer

Yes, thank you for taking the time to explain all of that. I appreciate it, because this question has been giving me a hard time!

callisto · Answer

you're welcome :) there is another case.. That is you cannot solve of the 2 equations, which means that there is no intercept between 2 lines, ie they are parallel to each other