What we have is one equation with two variables. So , we can not find a single solution for the equation. The solution will be unlimited values for x and y with a ratio between both variables.
The x values are any real number r
and y values are 4+(3/2)r , where r any real number.
To solve -3x+y= 8.
This is a single equation for two variables. So for a given y you can get the x value by:
-3x = 8-2y . Or
x = (8-2y)/(-3) = (2y-8)/3.
So for y = 6, x = (2y-8)/3 = (2*6-8)/3 = 4/3
Similarly, for a given x you can get the value of y from the equation:
2y = 8+3x. Or
y = (8+3x)/2.
If x = 10, y = (8+3x)/2 = (8+2*10)/2 = 14
More over, -3x+2y = 8, or 3x-2y+8 = 0 represents the graph of a sraight line and as such the (x,y) coordinates of every point onthis graph ofstraight line is a solution that satisfies the equation, -3x+2y = 8, or 3x-2y +8 =0. The line passes through the intercept (-8/3, 0) and (0,4). Or intercepts X axis at -8/3 and y axis at 4 units making a slope of 3/2 with x axis.