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you know whats really funny i was only doing this in class today, yet i cant remember it so im sorry i cant help i thouhgt i could but i couldnt

5x - 3y = 12

ax + by = 4

Substitute -3/2 to b.

5x - 3y = 12

ax (-3/2)y = 4

Convert both equations to y = mx + b.

5x - 3y = 12

-3y = -5x + 12 (Divide all terms by -3)

y = (5/3)x - 4

Since the slope in the other equation is 5/3, the slope in the other equation must also be 5/3.

ax (-3/2)y = 4

(-3/2)y = - ax + 4

Since the unknown slope has a negative sign attached to it, we should attach a negative sign to 5/3 as we find a.

To get the correct slope, we must multiply -5/3 by the unsimplified y to get the number which, when divided by -3/2, results to 5/3.

a = -5/3 * -3/2

a = 15/6 or 5/2 (Answer)

Checking:

ax - (3/2)y = 4

5/2 - (3/2)y = 4

(-3/2)y = -5/2 + 4 (Divide both sides by -3/2)

y = (5/3)y - 8/3

The equation is parallel with the other, since they have the same slope. Thus, our intuition is correct. a = 5/2 or 2.5 (Answer)

Hope this helps.

convert these equations into slope intercept form

5x - 3y = 12

=> y = 5x/3 - 12/3

=> y = (5/3)x - 4

Note in slope intercept form the co-efficient of x is the slope of equation and the slope of parallel equations is equal

similarly

ax + by = 4

=> y = (-a/b)x + 4/b

since lines are parallel

5/3 = -a/b

put b = -3/2

5/3 = -a * - 2/3

=> 5 = 2a

=> a = 5/2

First of all write the equation in slope intercept form y = mx + b

5x - 3y = 12

3y = 5x - 12

Divide by 3

y = 5/3 x - 3

To make the lines parallel, slope should be = 5/3

-a divided by -3/2 should be equal to -5

because in those equations

y = -5x+4

y = -ax-4/b

a = -15/2

by inspection a = 2.5