solve sytems of linear equations

Question

solve  8x - 6y = 14

 and  12x -9y = 18

 

 

 

show steps

Answer 1

Hi L;

I would like to add to what Jim S. explained.

8x - 6y = 14
12x -9y = 18

Both equations are in STANDARD FORM...

Ax+Bx=C, neither A nor B equal zero, and A is greater than zero.

Jim converted the equations to SLOPE-INTERCEPT FORM...

y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0.

FIRST EQUATION...

8x - 6y = 14

If we subtract 8x from both sides...

-6y=-8x+14

If we divide both sides by -6...

y=[(-8/-6)x]+(14/-6)

y=[(4/3)x]-(7/3)

SECOND EQUATION...

12x -9y = 18

If we subtract 12x from both sides...

-9y=-12x+18

If we divide both sides by -9...

y=[(-12/-9)x]+(18/-9)

y=[(4/3)x]-2

 

The y-intercept of the first equation is -7/3.

The y-intercept of the second equation is -2.

 

The slope of both equations is 4/3.

 

These are parallel lines which cannot be resolved.

Answer 2

If you rearrange these two equations showing y in terms of x you get:

 

y=(4x/3)-7/3 and y=(4x/3)-2 from this you can see that the slopes (coefficient of x) are equal (4/3) therefore the lines are parallel and can not intersect so there is no solution.

 

Regards

Jim S.

Fairport NY