solve the system by any method: x = 3/2y + 3 and 2x - 3y =6?

Answer 1

Substitute for x 2x-3y = 6 x = (6+3y)/2

x = 3/2y +3 = (6+3y)/2 Multiply both sides of the equation by 2y

3 + 6y = 6y +3y^ y^ = 0 y = 0 and x= 3

Proof :- 2x - 3y = 6 i.e. 2 x 3 - 3 x 0 = 6

Answer 2

x-3/2y=3
2x-3y=6

I would use linear combination unless you have studied matricies.
linear combination:

x-3/2y=3 // multiply the top one by -2 and add it to the
2x-3y=6 bottom one to cancel the x
--------------
0=0

when you get an answer that is ALWAYS true (like 0 = 0) the lines are the exact same, if you get a statement that is NEVER true (like 1 = 3) the lines do not intersect. (they must be plaallel and not the same line)

Answer 3

2x - 3y = 6
x - 3y/2 = 3
By inspection each equation is the same; hence, you do not have two equations to solve two unknowns. The best you can do is to solve for y:
2x-3y=6
-3y=6-2x
y=-2+2x/3 a straight line

Answer 4

(x - 3/2y = 3
(2x - 3y =6

Equation I: x = 3 + 3/2y
Equation II:
2(3 + 3/2y) - 3y = 6
6 + 3y - 3y = 6
0y = 6-6
It's impossible to solve.
<>>

Answer 5

x=3/2y+3 ------------ equ 1
2x-3y=6 -------------equ2

solution:

2x = 3y + 6
=> x = 3y/2 + 3
sub in equ 1
3y/2 + 3 = 3/2y + 3

cancel 3 on both sides,
3y/2 = 3/2y

cancel 3/2 on both sides
y = 1/y

cross multiplication
y^2 = 1
y = sqrt (1)
y=1 or -1.

if y=1, then x = 3/2 +3 // in equ 1
x=9/2
if y=-1, then x = -3/2 + 3 // in equ 1
x=3/2.

Answer 6

The 1-st and the 2-nd equations are equavalent, so you only have one (no matter which). From one equation you can find how x depends from y (or y from x). so, the answer is
x = x
y = (2/3)*x - 2

Yes, y = (2/3)*x - 2 is straight line , and she is infinite, so there are infinite number of answers.
(Get whatever you want x and put it to equation - you will get y, ans so on).

The answer we can write like that - { x ; (2/3)*x-2 }

Answer 7

It is not possible to solve only one equation with 2 variables.