Graphically the solutions are just the points on the line 4x

Graphically, the solutions are just the points on the line 4x + 2y-4: 4 -3 -2 2. Enter three particular solutions and then the general solution of the equation 2x+3y =-4. Enter particular solutions in the form (x,y). Example: (5,-8) First particular solution: (-2,0) Second particular solution: (1,-2) Check Clear Free Hint Check Clear Free Hint Check Clear Free Hint Third particular solution: (-1/2,-1) Enter general solution as (x,y(x)) where x) is a function of x. General solution: Check ClearFree Hint

Solution

2, The graph is only illustrative. The graph only illustrates that the solution of the equation will lie on the line. The paricular solutions of the equation 2x + 3y = -4 can be obtained by substituting arbitrary values of x like -2, 1, -1/2 and determining the corresponding values of y from the equation:

i. When x = - 2, we have 2(- 2)+3y = - 4or, -4 + 3y = -4 or, 3y = 0 so that y = 0. Thus one paricular solution is (-2,0)

ii. When x = 1, we have 2(1)+3y = - 4 or, 2 + 3y = -4 or, 3y = -6 so that y = -2 Thus 2nd paricular solution is (1, -2)

iii. When x = -1/2, we have 2(-1/2)+3y = - 4 or, -1 + 3y = -4 or, 3y = -3 so that y = -1Thus 3rd paricular solution is ( ( - 1/2, - 1).

The general solution can be found by seperating the terms of x and y. We have 2x + 3y = -4 or, 3y = - 4 - 2x or, y = - 4/3 - 2/3x. Thus, the general solution is ( x, - 4/3 - 2/3x)