Question

1.solve the following equation for y 3x- 2y= 6

Answer 1

So,

For number one, there will be an infinite number of solutions, as there are two placeholders.
3x - 2y = 6
It seems we can use the intercept method.
3x - 2(0) = 6
3x = 6

Divide both sides by 3
x = 2

This is one solution: (2,0)

3(0) - 2y = 6
-2y = 6

Divide both sidees by -2
y = -3

This is another solution: (0,-3)
You should now be able to draw the line.
If you want intercept form for this equation, just manipulate the equation in order to get the y = mx + b form.

Subtract 3x from both sides
-2y = -3x + 6

Divide both sides by -2
$y = \frac{3}{2} x + 6$


For the second problem, simply manipulate the equation.
$\frac{1}{3} (6x - 9) = \frac{3}{4} (4x - 8)$

Distribute
$2x - 3 = 3x - 6$

Subtract 2x from both sides
$-3 = x - 6$

Add 6 to both sides
$3 = x$


For the third problem, do the same thing.
$\frac{3(2x-1)}{4} = x + \frac{7}{2}$

We must first multiply both sides by 4.
$3(2x-1) = 4x + 14$

Distribute
$6x - 3 = 4x + 14$

Subtract 4x from both sides
$2x - 3 = 14$

Add 3 to both sides
$2x = 17$

Divide both sides by 2
$x = \frac{17}{2} \ or\ 8 \frac{1}{2}$