Hey there!
To start, first solve the equation of -2x + 3y =4 for the value of x since the coefficients appear to be smaller and easier to work with than the equation 4x- 6y= 9.
To solve -2x+3y=4 for x, first subtract both sides by 3y to isolate -2x:
-2x+3y=4
-2x=-3y+4
Now, divide both sides by -2 to isolate or solve for the x variable:
-2x=-3y+4
x=3/2y-2
Now that you have x set equal to the expression 3/2y-2, substitute this value for x in the equation 4x-6y=9:
x=3/2y-2
4x-6y=9
4(3/2y-2)-6y=9
Now, simplify this expression and combine your like terms:
4(3/2y-2)-6y=9
(4*3/2y)+(4*-2)-6y=9
6y-8-6y=9
-8=9
Because you end up in an untrue mathematical statement, your answer would be that there are no real solutions for this system.
Hope this helps and have a marvelous day! :)
