# -3x+2y=8 how do you solve it

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

-3x+2y= 8

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.

-3x+2y=8

==>  2y=8+3x

==> y=4+(3/2)x

The x values are any real number r

and y values are 4+(3/2)r , where r any real number.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve -3x+y= 8.

Solution:

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.