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.
